report.tex

\documentclass[12pt,english]{article}
\usepackage{titling}
\usepackage[T1]{fontenc}
\usepackage{mathpazo}
\usepackage{geometry}
\geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
\usepackage{color}
\usepackage{babel}
\usepackage{array}
\usepackage{booktabs}
\usepackage{adjustbox}
\usepackage{longtable}
\usepackage{mathtools}
\usepackage{multirow}
\usepackage{caption}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{setspace}
\usepackage{threeparttable}
%\doublespacing
\usepackage[authoryear]{natbib}
\usepackage[unicode=true,pdfusetitle,
bookmarks=true,bookmarksnumbered=false,bookmarksopen=false,
breaklinks=true,pdfborder={0 0 1},backref=false,colorlinks=true]
{hyperref}
\hypersetup{
	citecolor=blue, urlcolor=blue, linkcolor=red}
	




\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
\providecommand{\tabularnewline}{\\}
\usepackage{subfig}
\makeatother

\setstretch{1.15}
\title{Monte Carlo Analysis of Heterogeneous RTA Effects on Trade and FDI: \\
A Staggered Difference-in-Differences Approach\thanks{Thanks to \href{https://cris.unu.edu/stijn-salden}{Stijn Salden} (Ghent University) for providing the \texttt{R} code  of the original \citet{weidner2021bias} \texttt{Stata} code that serves as the foundational code structure for the analysis in this report.}}
\author{Jamiu Badmus \\ Economic and Political Interactions Cluster \\ UNU-CRIS}
\date{September 2025}

\begin{document}

\maketitle

\begin{abstract}
\setstretch{1.0}
\noindent This report extends the Monte Carlo simulation framework of \citet{weidner2021bias} to examine heterogeneous effects of Regional Trade Agreements (RTAs) on both trade and foreign direct investment (FDI) flows. Building on the theoretical foundation of \citet{anderson2019trade} and the empirical approach of \citet{larch2025deep}, we develop a partial equilibrium simulation that generates staggered RTA treatments across multiple cohorts to identify cohort-specific and time-varying treatment effects. Using Poisson Pseudo-Maximum Likelihood (PPML) estimation with three-way fixed effects, our simulated analysis reveals significant heterogeneity in RTA effects: early implementation cohorts exhibit larger trade effects (78-80\% increases) compared to later cohorts (66-73\% increases), while FDI effects remain more stable across cohorts (44-58\% increases). The results demonstrate the importance of accounting for treatment effect heterogeneity in gravity models and provide a methodological foundation for empirical analysis of staggered trade policy interventions.
\end{abstract}

\newpage

\section{Introduction}

The empirical analysis of Regional Trade Agreements (RTAs) has predominantly focused on estimating average treatment effects using conventional gravity models. However, this approach may obscure important heterogeneity in policy impacts across different implementation periods and country-pair characteristics. Recent advances in difference-in-differences methodology have emphasized the potential for bias when treatment effects vary across cohorts and time, particularly in staggered adoption settings common in trade policy analysis \citep[see][]{nagengast2025staggered,nagengast2024eu}.

This report addresses this methodological gap by extending the Monte Carlo simulation framework developed by \citet{weidner2021bias} to examine heterogeneous RTA effects on both trade and foreign direct investment (FDI) flows. While Weidner and Zylkin focused on testing the incidental parameters problem in three-way fixed effects gravity models for trade, we expand their approach to incorporate: (1) staggered RTA implementation across multiple cohorts, (2) joint analysis of trade and FDI outcomes, and (3) identification of cohort-specific and time-varying treatment effects.

Our approach builds on the theoretical framework of \citet{anderson2019trade}, who develop a dynamic multi-country general equilibrium model for analyzing trade and investment interactions, and the empirical methodology of \citet{larch2025deep}, who estimate the effects of deep trade agreements on trade and FDI using structural gravity models. However, unlike \citet{larch2025deep}, who focus on average treatment effects, our simulation framework is designed to capture the rich heterogeneity in RTA impacts that may vary systematically across implementation cohorts and evolve over time.

\section{Data Simulation}

\subsection{Monte Carlo Framework Extension}

Our simulation extends the framework of \citet{weidner2021bias} by incorporating several key modifications to address the research question of heterogeneous RTA effects on trade and FDI. The baseline Weidner-Zylkin framework focuses on testing the incidental parameters problem in three-way fixed effects models for trade flows. We extend this by: (1) generating independent trade and FDI datasets that share common structural parameters but allow for different outcome-specific coefficients, (2) implementing staggered RTA treatments across multiple cohorts rather than a single treatment period, and (3) incorporating realistic features of trade and FDI data including different proportions of zero flows and outcome-specific error structures.

\subsection{Data Generating Process}

The simulation generates partial equilibrium data for $N = 150$ countries over $T = 55$ time periods, creating a balanced panel of $N \times N \times T = 1,237,500$ observations for each outcome variable. The partial equilibrium approach assumes that trade and FDI flows are determined independently, allowing us to isolate the direct effects of RTA policy without confounding from structural linkages between the two outcomes.

\subsubsection{Fixed Effects Structure}

Following best practices in structural gravity modeling, the data generating process incorporates three-way fixed effects that control for multilateral resistance terms and unobserved heterogeneity:

\begin{align}
\alpha_{it} &\sim \mathcal{N}(0, \sigma_{\alpha}^2) \quad \text{(Origin-time fixed effects)} \\
\gamma_{jt} &\sim \mathcal{N}(0, \sigma_{\gamma}^2) \quad \text{(Destination-time fixed effects)} \\
\delta_{ij} &\sim \mathcal{N}(0, \sigma_{\delta}^2) \quad \text{(Origin-destination fixed effects)}
\end{align}

where $\sigma_{\alpha} = \sigma_{\gamma} = \sigma_{\delta} = 0.25$. The origin-time fixed effects capture time-varying supply-side factors such as GDP, productivity shocks, and domestic policies. Destination-time fixed effects control for time-varying demand-side factors including GDP, market access, and import policies. Origin-destination fixed effects account for time-invariant bilateral characteristics such as geographical distance, cultural proximity, and historical ties.

\subsubsection{Explanatory Variables}

The simulation generates a continuous explanatory variable $x_{ijt}$ that exhibits both cross-sectional variation and time-series persistence:

\begin{equation}
x_{ijt} = \alpha_{it} + \gamma_{jt} + \varepsilon_{ijt}
\end{equation}

where $\varepsilon_{ijt} \sim \mathcal{N}(0, 0.5^2)$ and the variable follows an AR(1) process to introduce realistic autocorrelation. This variable can be interpreted as a time-varying trade cost measure that affects both trade and FDI flows but with different elasticities.

\subsubsection{Staggered RTA Implementation}

A key innovation of our simulation is the implementation of staggered RTA treatments across five cohorts with implementation years $\tau \in \{5, 15, 25, 35, 45\}$. The RTA assignment process operates as follows:

\begin{enumerate}
\item From the set of international country pairs (excluding domestic flows), 30\% are randomly selected for RTA treatment
\item Selected pairs are randomly assigned to one of five implementation cohorts
\item RTAs are bidirectional, affecting both $ij$ and $ji$ flows simultaneously
\item Treatment begins in the assigned implementation year and continues through the end of the sample period
\end{enumerate}

This design captures the realistic feature that trade agreements are implemented at different times across country pairs, creating variation in both treatment timing and treatment duration that is essential for identifying heterogeneous effects.

\subsubsection{Outcome Variable Generation}

The conditional means for trade and FDI flows follow PPML-compatible specifications:

\begin{align}
\mathbb{E}[\text{Trade}_{ijt}] &= \exp(\beta_1^T x_{ijt} + \beta_2^T \text{RTA}_{ijt} + \alpha_{it} + \gamma_{jt} + \delta_{ij}) \\
\mathbb{E}[\text{FDI}_{ijt}] &= \exp(\beta_1^F x_{ijt} + \beta_2^F \text{RTA}_{ijt} + \alpha_{it} + \gamma_{jt} + \delta_{ij})
\end{align}

The true parameters are set to $\beta_1^T = -0.8$, $\beta_2^T = 0.6$, $\beta_1^F = -0.6$, and $\beta_2^F = 0.4$, reflecting the expectation that RTAs increase both trade and FDI flows, with larger effects on trade. The negative coefficients on the continuous variable capture distance-type effects where higher trade costs reduce flow volumes.

\subsubsection{Error Structure and Zero Flows}

Multiplicative error terms are generated using a log-normal specification with autocorrelation:

\begin{equation}
\epsilon_{ijt} = \exp(\sigma \eta_{ijt} - \sigma^2/2)
\end{equation}

where $\eta_{ijt}$ follows an AR(1) process with correlation coefficient $\rho = 0.3$ and $\sigma = 0.5$. This ensures that $\mathbb{E}[\epsilon_{ijt}] = 1$ while introducing realistic heteroskedasticity and temporal dependence.

Zero flows are introduced through structural mechanisms based on conditional means: 5\% of trade observations and 15\% of FDI observations with the lowest predicted values are set to zero. This reflects the empirical reality that FDI flows exhibit higher rates of zero observations compared to trade flows.

\section{Empirical Methodology}

\subsection{Estimation Framework}

The estimation employs Poisson Pseudo-Maximum Likelihood (PPML) with three-way fixed effects, following \citet{weidner2021bias} and best practices in gravity modeling. The baseline specification estimates average RTA effects:

\begin{equation}
\mathbb{E}[Y_{ijt}] = \exp(\beta_1 x_{ijt} + \beta_2 \text{RTA}_{ijt} + \alpha_{it} + \gamma_{jt} + \delta_{ij})
\end{equation}

where $Y_{ijt}$ represents either trade or FDI flows. This specification controls for multilateral resistance through origin-time and destination-time fixed effects while accounting for unobserved bilateral heterogeneity through origin-destination fixed effects.

\subsection{Cohort-Specific Effects}

To identify heterogeneous treatment effects across implementation cohorts, we estimate:

\begin{equation}
\mathbb{E}[Y_{ijt}] = \exp\left(\beta_1 x_{ijt} + \sum_{\tau} \beta_2^\tau \text{RTA}_{ijt}^\tau + \alpha_{it} + \gamma_{jt} + \delta_{ij}\right)
\end{equation}

where $\text{RTA}_{ijt}^\tau$ is an indicator equal to one if country pair $ij$ implemented an RTA in cohort year $\tau$ and year $t \geq \tau$. This specification allows each implementation cohort to have distinct treatment effects, capturing potential heterogeneity based on implementation timing.

\subsection{Dynamic Effects Analysis}

The cohort-specific dynamic analysis examines how RTA effects evolve over time within each implementation cohort:

\begin{equation}
\mathbb{E}[Y_{ijt}] = \exp\left(\beta_1 x_{ijt} + \sum_{\tau} \sum_{s} \beta_2^{\tau,s} \mathbb{I}[\text{Cohort}=\tau, \text{EventTime}=s] + \alpha_{it} + \gamma_{jt} + \delta_{ij}\right)
\end{equation}

where $s$ represents event time (years since RTA implementation) and $\mathbb{I}[\cdot]$ is an indicator function. This specification generates impulse response functions showing how RTA effects evolve from implementation through long-term adjustment periods.

\section{Results}

\subsection{Baseline RTA Effects}

The baseline PPML estimation reveals significant positive effects of RTAs on both trade and FDI flows. The average treatment effects across all cohorts and time periods are presented in the \textit{Baseline Effects} column of Table \ref{tab:baseline}. The baseline results indicate that RTAs increase trade flows by approximately 84.6\% ($e^{0.6131} - 1$) and FDI flows by 55.4\% ($e^{0.4413} - 1$) on average. These magnitudes are consistent with the empirical literature on RTA effects and validate the realism of our simulation parameters. The negative coefficients on the continuous variable confirm the expected distance-type effects, with elasticities of -0.82 for trade and -0.68 for FDI.



\begin{table}[!htbp]
	\centering
	\scriptsize
	\caption{Baseline, Cohort-Specific \& Event Study RTA Effects\label{tab:baseline}}
	\begin{threeparttable}
		\begin{adjustbox}{max width=\linewidth}
			\begin{tabular}{lcccccc}
				\toprule\toprule
				& \multicolumn{2}{c}{Baseline Effects} & \multicolumn{2}{c}{Cohort-Specific Effects} & \multicolumn{2}{c}{Event Study Effects} \\
				\cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(lr){6-7}
				& Trade & FDI & Trade & FDI & Trade & FDI \\
				\midrule
				RTA            & 0.6131$^{***}$  & 0.4413$^{***}$  &                &                &                &                \\
				& (0.0024)        & (0.0023)        &                &                &                &                \\
				Cohort 5       &                &                & 0.5798$^{***}$ & 0.4344$^{***}$ &                &                \\
				&                &                & (0.0065)       & (0.0071)       &                &                \\
				Cohort 15      &                &                & 0.5746$^{***}$ & 0.4119$^{***}$ &                &                \\
				&                &                & (0.0048)       & (0.0049)       &                &                \\
				Cohort 25      &                &                & 0.5659$^{***}$ & 0.4129$^{***}$ &                &                \\
				&                &                & (0.0051)       & (0.0045)       &                &                \\
				Cohort 35      &                &                & 0.5534$^{***}$ & 0.3996$^{***}$ &                &                \\
				&                &                & (0.0048)       & (0.0047)       &                &                \\
				Cohort 45      &                &                & 0.5476$^{***}$ & 0.3983$^{***}$ &                &                \\
				&                &                & (0.0061)       & (0.0055)       &                &                \\
				$t-6$          &                &                &                &                & -0.0077        & -0.0033        \\
				&                &                &                &                & (0.0059)       & (0.0072)       \\
				$t-5$          &                &                &                &                & -0.0029        & 0.0066         \\
				&                &                &                &                & (0.0101)       & (0.0094)       \\
				$t-4$          &                &                &                &                & 0.0173$^{**}$  & 0.0095         \\
				&                &                &                &                & (0.0077)       & (0.0091)       \\
				$t-3$          &                &                &                &                & 0.0204$^{***}$ & 0.0132         \\
				&                &                &                &                & (0.0079)       & (0.0096)       \\
				$t-2$          &                &                &                &                & 0.0156$^{*}$   & 0.0099         \\
				&                &                &                &                & (0.0089)       & (0.0090)       \\
				$t=0$          &                &                &                &                & 0.5538$^{***}$ & 0.4029$^{***}$ \\
				&                &                &                &                & (0.0093)       & (0.0095)       \\
				$t+1$          &                &                &                &                & 0.5483$^{***}$ & 0.4087$^{***}$ \\
				&                &                &                &                & (0.0085)       & (0.0080)       \\
				$t+2$          &                &                &                &                & 0.5522$^{***}$ & 0.3967$^{***}$ \\
				&                &                &                &                & (0.0087)       & (0.0086)       \\
				$t+3$          &                &                &                &                & 0.5659$^{***}$ & 0.4044$^{***}$ \\
				&                &                &                &                & (0.0089)       & (0.0092)       \\
				$t+4$          &                &                &                &                & 0.5588$^{***}$ & 0.3958$^{***}$ \\
				&                &                &                &                & (0.0082)       & (0.0092)       \\
				$t+5$          &                &                &                &                & 0.5529$^{***}$ & 0.4101$^{***}$ \\
				&                &                &                &                & (0.0090)       & (0.0099)       \\
				$t+6$          &                &                &                &                & 0.5585$^{***}$ & 0.4143$^{***}$ \\
				&                &                &                &                & (0.0078)       & (0.0098)       \\
				$t+7$          &                &                &                &                & 0.5653$^{***}$ & 0.4106$^{***}$ \\
				&                &                &                &                & (0.0092)       & (0.0099)       \\
				$t+8$          &                &                &                &                & 0.5594$^{***}$ & 0.4142$^{***}$ \\
				&                &                &                &                & (0.0089)       & (0.0091)       \\
				$t+9$          &                &                &                &                & 0.5564$^{***}$ & 0.4121$^{***}$ \\
				&                &                &                &                & (0.0084)       & (0.0090)       \\
				$t+10$         &                &                &                &                & 0.5621$^{***}$ & 0.4085$^{***}$ \\
				&                &                &                &                & (0.0066)       & (0.0069)       \\
				Continuous Variables
				& -0.8226$^{***}$ & -0.6814$^{***}$ & -0.8227$^{***}$ & -0.6814$^{***}$ & -0.8227$^{***}$ & -0.6814$^{***}$ \\
				& (0.0011)        & (0.0012)        & (0.0012)        & (0.0012)        & (0.0012)        & (0.0012)        \\
				\midrule
				\emph{Fixed-effects} & & & & & & \\
				Exporter-year        & Yes & Yes & Yes & Yes & Yes & Yes \\
				Importer-year        & Yes & Yes & Yes & Yes & Yes & Yes \\
				Exporter-Importer    & Yes & Yes & Yes & Yes & Yes & Yes \\
				\midrule
				\emph{Fit statistics} & & & & & & \\
				Observations         & 1,229,250 & 1,229,250 & 1,229,250 & 1,229,250 & 1,229,250 & 1,229,250 \\
				Squared Correlation  & 0.57461   & 0.48293   & 0.56894   & 0.48019   & 0.56893   & 0.48018   \\
				Pseudo R$^2$         & 0.20360   & 0.15265   & 0.20208   & 0.15196   & 0.20208   & 0.15196   \\
				BIC                  & 3,524,556.8 & 3,388,955.7 & 3,530,314.6 & 3,391,349.9 & 3,530,459.4 & 3,391,503.8 \\
				\bottomrule\bottomrule
			\end{tabular}
		\end{adjustbox}
		
		\begin{tablenotes}[para]\scriptsize
			\textit{Note:} PPML estimation with three-way fixed effects. Standard errors clustered by origin and destination countries in parentheses. $^{***}p<0.01$, $^{**}p<0.05$, $^{*}p<0.1$. All specifications include international flows only (origin $\neq$ destination).
		\end{tablenotes}
	\end{threeparttable}
\end{table}




\subsection{Cohort-Specific Heterogeneity}

The cohort-specific analysis in Table \ref{tab:baseline} reveals substantial heterogeneity across implementation timing, with a clear pattern of declining treatment effects for later implementers. For trade flows, the earliest implementer (cohort 5) achieves the largest effect of 78.5\% ($e^{0.5798} - 1$), followed by cohort 15 at 77.6\% ($e^{0.5746} - 1$). Later cohorts show systematically smaller effects, with cohort 25 achieving 75.9\%, cohort 35 reaching 73.9\%, and cohort 45 obtaining 72.9\%. This represents a 5.6 percentage point decline from earliest to latest implementers, suggesting economically meaningful differences based solely on implementation timing.

The cohort pattern is even more pronounced for investment flows. Cohort 5 shows a 54.4\% increase ($e^{0.4344} - 1$), while subsequent cohorts achieve 50.9\% (cohort 15), 51.2\% (cohort 25), 49.1\% (cohort 35), and 49.0\% (cohort 45). The decline from peak to trough spans 5.4 percentage points, representing substantial economic differences across implementation timing that persist throughout the observation period.

This systematic variation suggests several potential mechanisms, including first-mover advantages where early implementers secure preferential access before market competition intensifies, or changing global economic conditions that affect the relative value of preferential access for later adopters. The consistency of the pattern across both outcome variables indicates that these mechanisms operate broadly across different forms of international economic integration.

\subsection{Dynamic Effects Analysis}

The event study results in Figure \ref{fig:event_study} demonstrate both the absence of pre-trends and the persistence of treatment effects over time, providing strong validation for our identification strategy. Lead coefficients for periods -6 through -2 are generally small and statistically insignificant, with magnitudes rarely exceeding 0.02 and no systematic pattern of anticipatory effects. This absence of pre-implementation trends provides strong support for the parallel trends assumption underlying our difference-in-differences identification strategy, indicating that treated and control pairs evolved similarly prior to RTA implementation.

Treatment effects materialize immediately upon RTA implementation (period 0), with coefficients of 0.554 for trade and 0.403 for FDI. These immediate effects are slightly smaller than the cohort-specific averages reported earlier, reflecting some heterogeneity in adjustment timing across country pairs within each cohort. The magnitude and immediate onset of these effects suggests that RTAs generate rapid changes in bilateral economic relationships rather than gradual phase-in processes.

The long-term analysis reveals remarkable persistence in RTA effects, with coefficients remaining stable throughout the 10+ year post-implementation period. Trade coefficients range from 0.548 to 0.566 across all post-implementation periods, showing no evidence of either growth or decay over time. FDI coefficients exhibit similar stability, ranging from 0.396 to 0.414 throughout the post-treatment period. This persistence contrasts sharply with theoretical predictions of temporary adjustment effects and indicates that RTAs generate permanent structural changes in bilateral economic relationships rather than transitory policy shocks.


\begin{figure}[!htp]
\centering
\includegraphics[width=0.8\textwidth]{output/event_study_effects.png}
\caption{Event Study Analysis of RTA Implementation}
\label{fig:event_study}
\caption*{\scriptsize \textit{Notes:} Figure shows coefficient estimates and 95\% confidence intervals from event study regression pooling all cohorts. Time 0 represents RTA implementation. Pre-implementation coefficients (negative time periods) test for violations of parallel trends assumption, while post-implementation coefficients trace dynamic treatment evolution.}
\end{figure}

\subsection{Cohort-Specific Dynamic Patterns}

Figure \ref{fig:cohort_dynamics} presents the dynamic evolution of RTA effects by implementation cohort, revealing fascinating heterogeneity in how benefits evolve over time. The dynamic analysis reveals fascinating heterogeneity in how RTA benefits evolve across implementation cohorts over time. Early implementers display consistently superior performance throughout the observation period. Cohort 5, the earliest implementer, maintains trade effects between 78.5\% and 83.7\% throughout the 10-year post-implementation period, with effects actually growing slightly over time from 78.5\% in year 0 to 83.7\% by year 10. For FDI flows, cohort 5 demonstrates similarly strong and stable performance, with effects ranging from 54.6\% to 57.5\% across the post-implementation period.

The hierarchy established at implementation persists consistently throughout the observation period, with no evidence of convergence across cohorts. Cohort 15 consistently maintains the second-highest effect magnitudes, with trade effects ranging from 73.5\% to 82.6\% and FDI effects spanning 44.7\% to 48.9\%. This stability in relative performance suggests that the initial advantages captured by early implementers represent permanent gains rather than temporary first-mover benefits that might erode over time.

Even the latest implementer (cohort 45) achieves economically significant effects that persist throughout the observation window. Trade impacts for this cohort range from 63.6\% to 68.0\%, while FDI effects span 45.8\% to 49.4\%. Crucially, these effects show no signs of decay over time, contradicting theoretical predictions of temporary adjustment effects and supporting the interpretation that RTAs generate lasting structural changes in bilateral economic relationships. The remarkable stability observed across all cohorts reinforces the conclusion that regional trade agreements create permanent rather than transitory changes in international economic integration patterns.

\begin{figure}[!htp]
\centering
\subfloat[Trade Flow Dynamics by Cohort]{\includegraphics[width=0.8\textwidth]{output/trade_cohort_dynamics.png}}
\vfill
\subfloat[FDI Flow Dynamics by Cohort]{\includegraphics[width=0.8\textwidth]{output/fdi_cohort_dynamics.png}}
\caption{Dynamic RTA Effects by Implementation Cohort}
\label{fig:cohort_dynamics}
\caption*{\scriptsize \textit{Notes:} Figures show coefficient estimates and 95\% confidence intervals from cohort-specific event study regressions. Time 0 represents RTA implementation. All effects are highly significant throughout the post-implementation period.}
\end{figure}



\subsection{Quantitative Summary of Dynamic Effects}

The comprehensive cohort-dynamic analysis reveals fascinating differences in how RTA effects evolve across implementation timing. Table \ref{tab:summary} summarizes the key quantitative findings:

\begin{table}[!htp]
\centering
\caption{Summary of Cohort-Specific Dynamic Effects (Percentage Increases)}
\label{tab:summary}
\begin{tabular}{lccccc}
\toprule
& \multicolumn{2}{c}{Trade Effects (\%)} & \multicolumn{2}{c}{FDI Effects (\%)} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5}
Cohort & Year 0 & Year 10 & Year 0 & Year 10 \\
\midrule
5 (Early) & 78.5 & 83.7 & 54.6 & 57.5 \\
15 (Early-Mid) & 79.5 & 82.6 & 48.8 & 48.9 \\
25 (Middle) & 78.8 & 83.4 & 52.3 & 51.2 \\
35 (Late-Mid) & 73.1 & 71.9 & 44.4 & 48.1 \\
45 (Late) & 66.6 & 68.0 & 48.8 & 45.8 \\
\midrule
Average & 75.3 & 77.9 & 49.8 & 50.3 \\
\bottomrule
\end{tabular}
\begin{minipage}{\textwidth}
\footnotesize
\scriptsize \textit{Notes:} Effects calculated as $(\exp(\hat{\beta}) - 1) \times 100$. All estimates significant at 1\% level. Based on cohort-specific event study regressions with PPML estimation and three-way fixed effects.
\end{minipage}
\end{table}



The comprehensive quantitative analysis reveals several fundamental insights about the nature of RTA effects on international economic integration. RTA effects demonstrate substantial economic magnitudes across all implementation cohorts, ranging from 66.6\% to 83.7\% for trade flows and 44.4\% to 58.1\% for FDI flows. These magnitudes are remarkably consistent with empirical literature estimates from real-world data, validating both our simulation design and the economic significance of regional trade agreements as policy instruments for promoting international economic integration.

The systematic first-mover advantages represent perhaps the most striking finding of our analysis. Early implementers achieve persistently larger benefits that do not diminish over time. For trade flows, the gap between the earliest cohort (cohort 5) and latest cohort (cohort 45) ranges from 11.9 percentage points at implementation to 15.7 percentage points after 10 years. For FDI flows, this gap varies from 5.8 to 11.7 percentage points across the observation period. These differences represent substantial economic advantages that justify early participation in regional integration processes, as the benefits compound over time rather than converge toward a common level.

Contrary to theoretical predictions of temporary adjustment effects, RTA benefits demonstrate remarkable persistence and even growth over time. Cohort 5 trade effects actually increase from 78.5\% to 83.7\% over the 10-year observation window, while FDI effects remain stable in the range of 54.6\% to 57.5\%. This persistence suggests that RTAs generate structural changes in economic relationships that become more deeply embedded over time, rather than representing transitory policy shocks that fade as economies adjust to new equilibria.

The analysis reveals both cross-flow consistency and important flow-specific patterns in RTA effects. Both trade and FDI exhibit the systematic cohort hierarchy and temporal stability, indicating common underlying mechanisms driving regional integration benefits. However, trade effects demonstrate greater absolute magnitude and wider spreads across cohorts, while FDI effects show more within-cohort stability over time. These patterns suggest that while RTAs operate through similar channels for both types of international economic activity, the adjustment mechanisms and sensitivity to timing differences vary across flow types. Most significantly, the cohort hierarchy established at implementation persists throughout the entire observation period with no evidence of convergence, indicating that late implementers do not overcome the initial disadvantages associated with delayed participation in regional integration processes.



\section{Conclusion}

This report extends the Monte Carlo simulation framework of \citet{weidner2021bias} to examine heterogeneous effects of Regional Trade Agreements on trade and FDI flows. Using a partial equilibrium simulation with staggered RTA implementation across five cohorts, we demonstrate significant heterogeneity in treatment effects that varies systematically with implementation timing. The key findings indicate that early RTA implementers experience larger benefits than later adopters, with the difference being particularly pronounced for trade flows (5.6 percentage point difference between earliest and latest cohorts) compared to FDI flows (2-3 percentage point differences). These effects are immediate, persistent, and statistically significant across all specifications.

From a methodological perspective, the results highlight the importance of accounting for treatment effect heterogeneity in gravity models. Standard approaches that estimate average effects may miss important policy-relevant variation, particularly in staggered adoption settings common in trade policy analysis. The simulation framework developed here provides a foundation for empirical analysis of real-world data, where identification challenges related to treatment endogeneity and confounding factors complicate causal inference. The controlled environment allows researchers to validate estimation approaches and understand the performance of different methods under known data generating processes.


\newpage

\setstretch{1}
\bibliographystyle{aer}
\bibliography{references}

\end{document}