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To Adopt or Not to Adopt: Heterogeneous Trade Effects of the Euro
\begin{frontmatter}
\title{To Adopt or Not to Adopt: Heterogeneous Trade Effects of the Euro\tnoteref{t1}}
\tnotetext[t1]{This version: January 31, 2026. This paper extends ``The European Union and Trade: The Average Treatment Effect of Adopting the Euro,'' a chapter from the author's doctoral dissertation that applied propensity score matching. Earlier versions were presented at several conferences, and we thank participants for valuable feedback. I thank Birol Kanik for helpful comments and discussions. Recent advances in causal machine learning enabled us to revisit the research question and estimate the heterogeneous treatment effects that were not feasible with earlier methods.}
\author[aws]{Harry Aytug}
\ead{[email removed]}
\address[aws]{Amazon Web Services}
\begin{abstract}
Two decades of research on the euro's trade effects have produced estimates ranging
from 4\% to 30\%, with no consensus on the magnitude. We find evidence that this
divergence may reflect genuine heterogeneity in the euro's trade effect across country pairs
rather than methodological differences alone. Using Eurostat data on 15 EU countries (12 eurozone members plus Denmark, Sweden, and the UK as controls) from
1995--2015, we estimate that euro adoption increased bilateral trade by 29\% on
average (14.1\% after fixed effects correction), but effects range from $-12\%$ to $+79\%$ across eurozone pairs. Core
eurozone pairs (e.g., Germany--France, Germany--Netherlands) show large gains,
while peripheral pairs involving Finland, Greece, and Portugal saw smaller or
negative effects, with some negative estimates statistically significant and
interpretable as trade diversion. Pre-euro trade intensity and GDP
account for over 90\% of feature importance in explaining this heterogeneity. Extending to EU28, we find evidence that crisis-era
adopters (Slovakia, Estonia, Latvia) pull down naive estimates to 4.3\%, but accounting
for fixed effects recovers estimates of 13.4\%, consistent with the EU15 fixed-effects baseline of 14.1\%.
Illustrative counterfactual analysis suggests non-eurozone members would have experienced varied
effects: UK (+33\%), Sweden (+22\%), Denmark (+19\%). The wide range of prior estimates
appears to be largely a feature of the data, not a bug in the methods.
\end{abstract}
\begin{keyword}
euro \sep currency union \sep trade \sep heterogeneous treatment effects \sep gravity model \sep synthetic control
\end{keyword}
\end{frontmatter}
\section{Introduction}
Two decades of research on the euro's trade effects have failed to reach consensus.
Gravity model estimates cluster around 4--6\%, while synthetic control studies find
effects as high as 30\% for specific country pairs. \citet{rose2016emu} shows that
larger datasets produce systematically larger estimates. \citet{gunnella2021impact}
attribute the divergence to methodological differences. We propose an alternative
explanation: the wide range may reflect genuine heterogeneity in treatment effects
across country pairs, which existing methods cannot capture.
Understanding this heterogeneity has direct policy relevance. Sweden, Denmark, and
the United Kingdom opted out of the eurozone, and policymakers in these countries
have periodically revisited the adoption question. If the euro's trade effects are
uniformly positive, the trade-based case for adoption is straightforward. But if effects vary
substantially---large for some pairs, near-zero for others---the calculus becomes
more complex. The same logic applies to prospective members in Central and Eastern
Europe. Knowing \textit{which} country pairs benefit most, and \textit{why}, is
essential for informed policy.
We estimate the full distribution of euro trade effects across all eurozone country
pairs. Our approach suggests substantial heterogeneity that may help reconcile the
divergent estimates in prior literature: gravity models, which estimate average effects,
capture the center of the distribution (around 20\%), while synthetic control
studies, which focus on specific high-trade pairs, capture the upper tail (30\%+)---precisely
because SCM studies typically select pairs where credible synthetic counterfactuals exist.
We also generate illustrative counterfactual predictions for non-eurozone EU members,
estimating what trade effects Sweden, Denmark, and the United Kingdom might have
experienced had they adopted the euro.
The EU provides a useful setting for this analysis because member countries meet
the Maastricht criteria for fiscal discipline, price stability, and exchange rate
stability, yet not all have adopted the euro. This creates a comparison
where the main observable difference between treatment and control groups is euro
adoption itself, though we acknowledge that unobserved differences may remain.
To our knowledge, this is among the first studies to estimate the full
distribution of heterogeneous treatment effects of currency union membership.
Methodologically, we use causal forests with double machine learning to estimate
conditional average treatment effects at the country-pair level.
The paper proceeds as follows. Section 2 reviews the literature on currency
unions and trade. Section 3 describes the causal forest methodology. Section 4
presents the data. Section 5 reports results on heterogeneous treatment effects.
Section 6 discusses the findings. Section 7 presents counterfactual analysis for
non-eurozone EU members. Section 8 concludes.
\section{Literature Review}
Research on the trade effects of common currencies began with the influential
contribution of \citet{rose2000money}, which used a gravity framework and
reported very large trade increases among currency-union members. This result
triggered extensive debate about identification, selection into currency unions,
and the credibility of cross-sectional comparisons. Addressing these concerns,
\citet{persson2001currency} applied matching-based reasoning and argued that
differences between treated and untreated pairs can generate substantial upward
bias in na\"{i}ve estimates.
A second wave of work emphasized panel variation and dynamics. For example,
\citet{bun2002euro} estimated a dynamic panel model focused on the euro and
found a modest short-run effect that accumulates over time. In parallel,
methodological advances in gravity estimation improved the interpretability of
currency-union coefficients. \citet{anderson2003gravity} formalized multilateral
resistance---showing that bilateral trade depends on relative trade costs---and
their framework became a benchmark for modern gravity specifications.
Direct evidence on the euro specifically emerged early. \citet{micco2003currency}
provided early EMU evidence using developed-country data and found positive trade
effects. Subsequent gravity work increasingly adopted estimation strategies
designed to handle heteroskedasticity and zero trade flows.
\citet{santossilva2006log} showed that log-linear OLS can be misleading under
heteroskedasticity and advocated PPML-type approaches that have since become
standard in gravity estimation.
Despite improvements in data and methods, estimates of the euro's trade effect
continued to vary. One explanation is that results are sensitive to data coverage
and specification choices: \citet{rose2016emu} documented that larger datasets
(more countries/longer spans) tend to deliver systematically larger EMU trade
estimates. A complementary explanation emphasizes that different empirical
approaches target different parameters. For example, \citet{gunnella2021impact}
compare gravity and synthetic control approaches and report modest ``average-type''
gravity effects alongside substantially larger effects for some pairs under
synthetic control.
A major methodological branch in this literature uses Synthetic Control Methods
(SCM), which construct a data-driven counterfactual from weighted donor units
and are particularly attractive when a small number of treated units receive a
discrete policy intervention. The approach is grounded in foundational
contributions such as \citet{abadie2010synthetic}. SCM has been applied both
within and beyond trade settings to study institutional and macro-financial
regime changes. \citet{aytug2017rom} uses SCM to construct counterfactual
exchange rate volatility in the absence of Turkey's Reserve Option Mechanism,
illustrating that policy effects can be strongly state-dependent and sensitive
to concurrent monetary tightening. In trade-policy evaluation,
\citet{aytug2017customs} apply SCM to assess the EU--Turkey Customs Union and
show sizable effects relative to a synthetic counterfactual. In the euro context,
\citet{saia2017uk} uses SCM to study the counterfactual of UK euro adoption and
finds sizable trade gains in that scenario.
At the same time, the SCM toolkit has expanded in ways that matter for
interpretation. \citet{benmichael2021augmented} propose the Augmented Synthetic
Control Method to improve performance when perfect pre-treatment fit is not
feasible. \citet{arkhangelsky2021sdid} introduce Synthetic Difference-in-Differences,
combining elements of DID and synthetic control to improve robustness in common
empirical settings. More recently, \citet{distefano2024inclusive} propose an
``inclusive'' synthetic control variant designed for settings where spillovers
or indirect effects may contaminate donor pools. These developments strengthen
the credibility of comparative-case approaches, but they also reinforce a core
limitation: SCM-style designs remain most naturally suited to case-specific
evaluation (one or a few treated units) rather than systematic characterization
of effects across the full set of euro-area country pairs.
This brings the literature to a central unresolved issue: heterogeneity. Gravity
models typically estimate an average (or average-like) effect of euro membership
across treated pairs, while SCM studies often focus on a subset of country-pairs
where credible synthetic counterfactuals can be built---precisely the setting in
which large effects are more likely to be detected. The combination of these
approaches therefore leaves open an important question: what is the full
distribution of the euro's trade effects across all euro-area pairs, and which
observable features predict where a given pair lies in that distribution?
To address this gap, we build on the growing literature that applies modern
causal inference tools to uncover treatment effect heterogeneity.
\citet{athey2016recursive} develop tree-based approaches designed specifically
for heterogeneous causal effects, providing a foundation for forest-based
estimators. Related work on machine-learning-based causal inference, such as
\citet{chernozhukov2018double}, provides tools for valid inference on causal
parameters in high-dimensional settings. Our contribution is to use these ideas
to estimate the distribution of euro trade effects across country pairs, thereby
reconciling why different methods in the existing literature can yield apparently
conflicting results.
Table~\ref{tab:comparison} summarizes the key methodological differences between
existing approaches and our causal forest method.
\begin{table}[!htbp]
\centering
\caption{Comparison of Estimation Approaches}
\label{tab:comparison}
\small
\begin{tabular}{@{}lccc@{}}
\toprule
& \textbf{Gravity/PSM} & \textbf{SCM} & \textbf{Causal Forest} \\
\midrule
Estimates & Single ATE & Few pair effects & Full CATE distribution \\
Heterogeneity & Pre-specified only & Not systematic & Data-driven discovery \\
Selection bias & PSM addresses & Matching-based & DML residualization \\
Inference & Clustered SE & Placebo tests & Forest-based CI \\
Literature range & 4--30\% & 16--30\% & --- \\
\bottomrule
\end{tabular}
\end{table}
\section{Methodology}
\subsection{Existing Approaches: Gravity and Synthetic Control}
The gravity model is the workhorse of empirical trade analysis. Following
\citet{anderson2003gravity} and best practices outlined in \citet{gunnella2021impact},
the structural gravity equation with a saturated set of fixed effects is:
\begin{equation}
\ln(X_{ijt}) = \lambda_{it} + \psi_{jt} + \mu_{ij} + \boldsymbol{\beta}'
\mathbf{z}_{ijt} + \gamma \text{CU}_{ijt} + \varepsilon_{ijt}
\end{equation}
where $X_{ijt}$ denotes exports from country $i$ to country $j$ at time $t$,
$\lambda_{it}$ and $\psi_{jt}$ are exporter-time and importer-time fixed effects
that control for multilateral resistance, $\mu_{ij}$ are pair fixed effects that
absorb time-invariant bilateral factors (distance, common language, contiguity),
$\mathbf{z}_{ijt}$ includes time-varying bilateral controls such as regional trade
agreements, and $\text{CU}_{ijt}$ is a dummy equal to one if both countries are in
a currency union at time $t$. The coefficient $\gamma$ captures the average
treatment effect of euro adoption. Estimation via PPML addresses heteroskedasticity
and zero trade flows \citep{santossilva2006log}.
The synthetic control method (SCM) offers an alternative approach by constructing
a counterfactual for each treated unit as a weighted combination of control units.
Following \citet{abadie2003economic}, the causal effect is estimated as:
\begin{equation}
\hat{\tau}_1 = \mathbf{y}_1 - \mathbf{y}_0^* = \mathbf{y}_1 - \mathbf{Y}_0 \mathbf{w}^*
\end{equation}
where $\mathbf{y}_1$ is the outcome vector for the treated unit, $\mathbf{Y}_0$ is
a matrix of outcomes for $J$ control units, and $\mathbf{w}^*$ is a vector of
weights chosen to minimize the distance between treated and synthetic control
units in the pre-treatment period. \citet{gunnella2021impact} apply SCM to
estimate euro effects for specific country pairs, finding effects around 30\%.
\citet{saia2017uk} uses SCM to estimate what UK trade would have been under euro
adoption, finding a 16\% effect. While SCM provides credible counterfactuals for
individual cases, it does not scale to estimate effects for all country pairs or
systematically explore heterogeneity.
Both approaches have limitations for our research question. Gravity models
estimate a single average effect, potentially masking substantial heterogeneity
across pairs. SCM can estimate pair-specific effects but requires selecting
cases ex ante and does not identify what drives variation. We propose causal
forests as a method that combines the strengths of both: estimating the full
distribution of treatment effects while identifying the characteristics that
explain heterogeneity.
\subsection{From PSM to Causal Forests}
Traditional propensity score matching (PSM) addresses selection bias by matching
treated and control units based on their probability of treatment. Following
\citet{persson2001currency}, the propensity score is defined as:
\begin{equation}
e(X) = P(\text{Euro}_{ijt} = 1 \mid X_{ijt})
\end{equation}
where $X_{ijt}$ includes GDP and other pair characteristics. The
average treatment effect on the treated (ATT) is then:
\begin{equation}
\tau_{\text{ATT}} = E[Y^{(1)} - Y^{(0)} \mid \text{Euro} = 1]
\end{equation}
While PSM addresses selection bias, it estimates only a single average effect.
Causal forests extend this framework by estimating heterogeneous treatment
effects --- allowing the effect to vary with observed characteristics:
\begin{equation}
\tau(x) = E[Y^{(1)} - Y^{(0)} \mid X = x]
\end{equation}
This Conditional Average Treatment Effect (CATE) captures how the euro's impact
varies across country pairs with different characteristics.
\subsection{Intuition: How Causal Forests Discover Heterogeneity}
Before presenting the technical details, we provide intuition for how causal
forests estimate heterogeneous treatment effects. The key insight is that
causal forests are designed to answer a different question than traditional
methods: rather than asking ``what is the average effect?'' they ask ``for
which units is the effect largest, and why?''
A standard decision tree predicts outcomes by recursively splitting the data
into groups that are most similar in their outcome values. A \textit{causal}
tree instead splits the data into groups that are most \textit{different} in
their treatment effects. Consider a simple example: if the euro's effect on
trade is larger for country pairs with high pre-existing trade intensity,
the causal tree will split on trade intensity, creating one group (high-trade pairs) with
a high estimated effect and another group (low-trade pairs) with a lower effect.
The algorithm proceeds as follows. At each node, the tree considers all possible
splits of the data (e.g., GDP above/below median, pre-euro trade high/low) and selects the
split that maximizes the difference in treatment effects between the resulting
subgroups. This process continues recursively until the subgroups become too
small. The treatment effect for any unit is then estimated as the average
effect within its terminal node (leaf).
A single tree would be noisy and sensitive to the particular sample. Causal
\textit{forests} address this by growing many trees (we use 500) on bootstrapped
samples and averaging their predictions. This ensemble approach reduces variance
while preserving the ability to capture complex heterogeneity patterns.
Two features distinguish causal forests from standard machine learning methods.
First, ``honest'' estimation uses separate subsamples for determining the tree
structure and estimating effects within leaves, preventing overfitting and
enabling valid statistical inference. Second, the algorithm provides not just
point estimates but confidence intervals for each unit's treatment effect,
allowing researchers to assess statistical significance at the individual level.
For our application, this means the causal forest can discover --- without
prior specification --- that the euro's trade effect is large for core European
pairs with deep existing trade relationships, modest for peripheral pairs, and
near-zero for pairs involving Greece. Traditional methods would require the
researcher to hypothesize these patterns in advance and test them through
subgroup analysis or interaction terms. Figure~\ref{fig:causal_tree} illustrates
this process.
\begin{figure}[!htbp]
\centering
\begin{tikzpicture}[scale=0.8, transform shape,
node distance=0.9cm and 0.5cm,
every node/.style={font=\footnotesize},
root/.style={rectangle, draw, rounded corners, minimum width=2.8cm, minimum height=0.7cm, align=center, fill=gray!20},
internal/.style={rectangle, draw, rounded corners, minimum width=2.2cm, minimum height=0.7cm, align=center, fill=blue!10},
leaf/.style={rectangle, draw, rounded corners, minimum width=1.8cm, minimum height=0.7cm, align=center},
high/.style={leaf, fill=green!25},
medium/.style={leaf, fill=yellow!25},
low/.style={leaf, fill=red!15}
]
\node[root] (root) {All EU Pairs\\$\hat{\tau} = +24\%$};
\node[internal, below left=0.9cm and 1.2cm of root] (left1) {High Pre-Euro Trade\\$\hat{\tau} = +50\%$};
\node[internal, below right=0.9cm and 1.2cm of root] (right1) {Low Pre-Euro Trade\\$\hat{\tau} = +8\%$};
\node[high, below left=0.8cm and 0.2cm of left1] (ll) {High GDP\\$\hat{\tau} = +77\%$};
\node[medium, below right=0.8cm and 0.2cm of left1] (lr) {Low GDP\\$\hat{\tau} = +35\%$};
\node[medium, below left=0.8cm and 0.2cm of right1] (rl) {High GDP\\$\hat{\tau} = +15\%$};
\node[low, below right=0.8cm and 0.2cm of right1] (rr) {Low GDP\\$\hat{\tau} = -3\%$};
\draw[-latex] (root) -- node[left, pos=0.5] {\tiny Yes} (left1);
\draw[-latex] (root) -- node[right, pos=0.5] {\tiny No} (right1);
\draw[-latex] (left1) -- node[left, pos=0.5] {\tiny Yes} (ll);
\draw[-latex] (left1) -- node[right, pos=0.5] {\tiny No} (lr);
\draw[-latex] (right1) -- node[left, pos=0.5] {\tiny Yes} (rl);
\draw[-latex] (right1) -- node[right, pos=0.5] {\tiny No} (rr);
\node[below=0.2cm of ll, font=\tiny, text=gray] {e.g., FR--LU};
\node[below=0.2cm of rr, font=\tiny, text=gray] {e.g., FI--IE};
\end{tikzpicture}
\caption{Illustration of causal tree splitting. The tree recursively partitions
country pairs into subgroups with different treatment effects. At each node,
the split is chosen to maximize the difference in euro effects between
subgroups. Terminal nodes (leaves) show estimated effects ranging from +77\%
for high-trade, high-GDP pairs (e.g., France--Luxembourg) to $-3\%$ for low-trade,
low-GDP pairs (e.g., Finland--Ireland).
Colors indicate effect magnitude: green (high), yellow (medium), red (low).
A causal forest averages predictions across many such trees.}
\label{fig:causal_tree}
\end{figure}
\subsection{Causal Forest with Double Machine Learning}
We apply Causal Forests with Double Machine Learning
\citep{athey2018estimation, chernozhukov2018double} to estimate the full
distribution of CATEs. The CausalForestDML estimator proceeds in three steps:
\medskip
\textbf{Step 1: Nuisance estimation.} Use machine learning to estimate:
\begin{align}
\hat{m}(W) &= E[Y \mid W] \quad \text{(outcome model)} \\
\hat{e}(W) &= E[T \mid W] \quad \text{(propensity score)}
\end{align}
\textbf{Step 2: Residualize.} Partial out the effect of controls:
\begin{align}
\tilde{Y} &= Y - \hat{m}(W) \\
\tilde{T} &= T - \hat{e}(W)
\end{align}
\textbf{Step 3: Causal forest.} Estimate $\tau(X)$ using an honest random forest
on the residualized data $(\tilde{Y}, \tilde{T}, X)$.
\medskip
This approach removes regularization bias from the ML first stage and provides
valid confidence intervals. It is doubly robust: consistent if either $\hat{m}$
or $\hat{e}$ is correctly specified. We implement CausalForestDML with Random
Forest first-stage models (200 trees, min\_samples\_leaf = 20), a causal forest
with 500 trees and honest splitting (min\_samples\_leaf = 30), and a Random
Forest Classifier for the binary treatment model.
\subsection{Constructing Counterfactuals}
A fundamental challenge in causal inference is that we never observe the
counterfactual outcome --- what trade would have been for a eurozone pair had
they not adopted the euro, or for a non-eurozone pair had they adopted it.
Using the potential outcomes framework, each unit has two potential outcomes:
$Y^{(1)}$ (outcome if treated) and $Y^{(0)}$ (outcome if not treated). The
treatment effect for unit $i$ is:
\begin{equation}
\tau_i = Y_i^{(1)} - Y_i^{(0)}
\end{equation}
We observe $Y_i^{(1)}$ for treated units and $Y_i^{(0)}$ for control units,
but never both for the same unit.
Traditional matching methods address this by finding ``twin'' control units
with similar observable characteristics to impute the missing potential outcome.
Causal forests take a different approach: they estimate the conditional average
treatment effect function $\tau(x) = E[Y^{(1)} - Y^{(0)} \mid X = x]$ from the
data, then apply this learned function to predict effects for any unit.
For a non-eurozone pair like UK--Germany with characteristics $x_{\text{UK-DE}}$,
the counterfactual prediction is:
\begin{equation}
\hat{\tau}(\text{UK-DE}) = \hat{\tau}(x_{\text{UK-DE}})
\end{equation}
The causal forest predicts what effect euro adoption \textit{would have had}
based on the pair's characteristics (GDP, pre-euro trade intensity)
and how similar characteristics related to treatment effects among eurozone
pairs. The key identifying assumption is that the CATE function learned from
treated units generalizes to untreated units with similar characteristics ---
formally, that $\tau(x)$ is the same for treated and untreated units conditional
on $X = x$.
\subsection{Treatment Definition and Identification}
We define the treatment as both countries in a pair having adopted the euro:
\begin{equation}
T_{ijt} = \mathbf{1}[\text{Euro}_i = 1] \times \mathbf{1}[\text{Euro}_j = 1]
\end{equation}
The sample is restricted to pairs where both countries are EU members, ensuring
all units faced a credible possibility of treatment. Countries outside the EU
(e.g., United States, Japan, Switzerland) could never adopt the euro and thus
do not constitute a valid counterfactual. Within the EU sample, eurozone members
(Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg,
Netherlands, Portugal, Spain) constitute the treatment group, while EU members
that opted out (Denmark, Sweden, United Kingdom) constitute the control group.
The outcome variable is log real bilateral trade:
\begin{equation}
Y_{ijt} = \ln\left(\frac{\text{Exports}_{ij} + \text{Imports}_{ij}}{\text{PPI}_t}\right)
\end{equation}
For PPML specifications in the gravity benchmark, we use trade in levels following \citet{santossilva2006log}.
Effect modifiers $X$ --- the variables that may drive heterogeneity in treatment
effects --- include log GDP product, log GDP per capita, and pre-euro trade intensity (average bilateral trade 1995--1998, the pre-treatment period in our sample).
Controls $W$ used in the first-stage nuisance estimation address potential
confounders that affect both euro adoption and trade:
\begin{itemize}
\item \textit{Log GDP product}: Larger economies trade more and were more
likely to be founding eurozone members.
\item \textit{Log GDP per capita}: Richer countries have different trade
patterns and faced different incentives for euro adoption.
\item \textit{Year}: Controls for business cycle effects and common time
trends; the DML residualization removes year-specific variation from
both outcome and treatment, analogous to year fixed effects.
\end{itemize}
Identification relies on the conditional independence assumption: conditional on
the controls $W$, treatment assignment is independent of potential outcomes. The
DML framework addresses selection on observables by flexibly modeling the
relationship between confounders and both the outcome and treatment. The causal
forest then estimates heterogeneous effects conditional on effect modifiers $X$,
which may overlap with but are conceptually distinct from the confounders $W$.
\subsection{Threats to Identification}
While the DML framework addresses selection on observables through flexible
first-stage estimation, our identification strategy faces potential threats
from unobserved confounders. We discuss the main concerns and the evidence
bearing on them.
Countries that adopted the euro may have had stronger political commitment
to European integration, which could independently affect trade through
non-tariff barrier reductions, regulatory harmonization, or business confidence.
However, all countries in our sample are EU members that met the Maastricht
criteria, suggesting similar baseline commitment to integration. The non-adopters
(UK, Sweden, Denmark) obtained formal opt-outs, reflecting specific domestic
political constraints rather than weaker commitment to European trade integration
per se. Denmark maintains a currency peg to the euro, demonstrating commitment
to monetary stability without formal adoption.
Higher-quality institutions might facilitate both euro adoption and trade
expansion. We partially address this by restricting the sample to EU members,
which share common institutional frameworks including the single market,
common external tariff, and harmonized regulations. The remaining variation
in institutional quality within the EU is modest compared to cross-country
studies that include developing economies.
Countries experiencing economic booms might have been more likely to adopt
the euro and to experience trade growth. We address this through year fixed
effects in the DML first stage, which remove common time trends. The EU15
sample benefits from synchronized adoption timing (1999--2001), limiting
variation in business cycle position at treatment. The EU28 extension, where
adoption timing varies with the 2008--2012 crisis, shows how business cycle
confounding can bias estimates downward---and how CFFE correction recovers
consistent estimates.
An ideal instrument would predict euro adoption but affect trade only through
the adoption channel. Potential instruments face validity concerns:
\begin{itemize}
\item \textit{Geographic proximity to Brussels}: Correlated with trade
through standard gravity channels
\item \textit{Historical currency arrangements}: Reflect deep economic
integration that directly affects trade
\item \textit{Referendum outcomes}: Endogenous to economic conditions and
trade expectations
\item \textit{Political party composition}: May affect trade policy
directly through non-monetary channels
\end{itemize}
Following \citet{barro2007economic}, who use the probability of independently
adopting a third country's currency as an instrument, we considered similar
approaches but found them inapplicable to the eurozone context where adoption
was a coordinated political decision rather than independent currency choices.
We provide two forms of evidence supporting the parallel trends assumption.
First, an event study analysis (Figure~\ref{fig:pre_trends}) shows that
pre-treatment coefficients (1995--1997) are small in magnitude ($-3\%$ to $-5\%$)
compared to post-treatment effects ($+8\%$ to $+24\%$), with a clear break at
1999 when effects become positive. Second, placebo tests (Figure~\ref{fig:placebo}) assigning fake
treatment dates (1995, 1997) find no significant ``effects,'' suggesting our
estimates do not reflect pre-existing differential trends.
Following \citet{oster2019unobservable}, we assess how much selection on
unobservables would be required to explain away our results (Table~\ref{tab:sensitivity}). The analysis
suggests that unobserved confounders would need to be substantially more
important than the observed confounders (GDP, GDP per capita, year) to reduce
the estimated effect to zero. Given that our controls capture the main economic
determinants of both euro adoption and trade, this degree of omitted variable
bias appears implausible.
Leave-one-out analysis (Figure~\ref{fig:leave_one_out}) dropping each country in turn shows that no single
country drives the results. The ATE remains stable within the confidence
interval of the full-sample estimate regardless of which country is excluded,
including Luxembourg (which has the largest estimated effects) and peripheral
economies like Greece and Portugal.
In summary, while we cannot definitively rule out all unobserved confounding,
the combination of (1) restricting to EU members with similar institutional
frameworks, (2) flexible DML adjustment for observable confounders, (3)
pre-trends evidence supporting parallel trends, (4) placebo tests finding no
spurious effects, and (5) sensitivity analysis suggesting implausible degrees
of omitted variable bias provides reasonable confidence in our identification
strategy.
\section{Data}
We use bilateral trade data from Eurostat, which provides comprehensive trade
statistics for EU member states. The dataset covers 15 EU countries (EU15) from
1995 to 2015, matching the methodology of \citet{gunnella2021impact}. While
Eurostat trade data extends back to 1988, GDP data from Eurostat's national
accounts becomes consistently available only from 1995, making earlier years
unsuitable for our analysis which requires GDP controls. We restrict
the sample to the EU15 (pre-2004 enlargement members) for two reasons. First,
recent euro adopters among the 2004+ enlargement countries have insufficient
post-treatment data: Slovenia joined in 2007 (8 years), Slovakia in 2009 (6 years),
Estonia in 2011 (4 years), Latvia in 2014 (1 year), and Lithuania in 2015 (0 years
in our sample). Second, this sample matches the sample used by \citet{gunnella2021impact}, enabling direct
comparison. The outcome, treatment, and control variables are
defined in Section 3.4.
The eurozone members in our sample are Austria, Belgium, Finland, France, Germany,
Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, and Spain. The
control group consists of EU members that did not adopt the euro: Denmark,
Sweden, and the United Kingdom. This design avoids reliance on non-European
donor countries, a common concern in early euro studies that used global samples.
Table~\ref{tab:summary_stats} reports summary statistics. Log real trade has a
mean of 22.30 with substantial variation (standard deviation of 1.73), reflecting
heterogeneity in bilateral trade flows across EU pairs. The euro adoption
indicator equals one for 51\% of observations, reflecting the balanced panel
structure with eurozone pairs observed both before and after 1999. Table~\ref{tab:sample_composition} shows the panel
contains 2,149 observations covering 105 unique country pairs across 15 countries.
Of these, 1,100 (51.2\%) are treated while 1,049 (48.8\%) serve as controls.
\begin{table}[h]
\centering
\caption{Summary Statistics}
\small
\begin{tabular}{@{}lcccc@{}}
\toprule
\textbf{Variable} & \textbf{Mean} & \textbf{Std. Dev.} & \textbf{Min} & \textbf{Max} \\
\midrule
Log real trade & 22.30 & 1.73 & 15.99 & 26.06 \\
Log GDP product & 25.74 & 1.61 & 21.37 & 29.73 \\
Log GDP per capita & 20.50 & 0.64 & 18.31 & 22.45 \\
EU membership & 1.00 & 0.00 & 1.00 & 1.00 \\
Euro adoption & 0.51 & 0.50 & 0.00 & 1.00 \\
\bottomrule
\end{tabular}
\label{tab:summary_stats}
\end{table}
\begin{table}[h]
\centering
\caption{Sample Composition}
\small
\begin{tabular}{@{}lr@{}}
\toprule
\textbf{Characteristic} & \textbf{Value} \\
\midrule
Total observations & 2,149 \\
Unique country pairs & 105 \\
Countries & 15 \\
Year range & 1995--2015 \\
\midrule
Treated (euro = 1) & 1,100 (51.2\%) \\
Control (euro = 0) & 1,049 (48.8\%) \\
\midrule
Mean bilateral trade & EUR 16.7B \\
Median bilateral trade & EUR 4.9B \\
\bottomrule
\end{tabular}
\label{tab:sample_composition}
\end{table}
Table~\ref{tab:covariate_balance} compares covariate means between eurozone and
non-eurozone pairs in the post-1999 period. Non-eurozone pairs (involving Denmark,
Sweden, or UK) have higher GDP per capita (standardized difference of $-0.46$) and
larger combined GDP ($-0.23$), reflecting that the non-euro EU members are relatively
wealthy economies. When covariate distributions differ
substantially between treated and control groups, OLS and gravity models rely on
linear extrapolation from regions of the covariate space where control
observations are sparse, potentially yielding biased and unstable estimates
\citep{baier2009estimating, persson2001currency}. \citet{baier2009estimating}
show that matching estimates of FTA treatment effects are much more stable and
economically plausible than OLS gravity estimates, which often display extreme
instability across years. This motivates our use of causal forests with
double machine learning, which extends the matching approach by flexibly
adjusting for covariate differences through nonparametric first-stage estimation
while also allowing treatment effects to vary with observed characteristics.
\begin{table}[h]
\centering
\caption{Covariate Balance: Eurozone vs.\ Non-Eurozone Pairs (Post-1999)}
\label{tab:covariate_balance}
\small
\begin{tabular}{@{}lcccc@{}}
\toprule
\textbf{Variable} & \textbf{Eurozone} & \textbf{Non-EZ} & \textbf{Diff.} & \textbf{Std.\ Diff.} \\
\midrule
Log bilateral trade & 22.27 & 22.42 & -0.15 & -0.09 \\
Log GDP product & 25.70 & 26.06 & -0.36 & -0.23 \\
Log GDP per capita & 20.56 & 20.81 & -0.24 & -0.46 \\
Pre-euro trade intensity & 22.10 & 22.23 & -0.13 & -0.09 \\
\bottomrule
\end{tabular}
\vspace{0.5em}
\footnotesize
\textit{Note:} Standardized difference $>$ 0.25 indicates meaningful imbalance.
Eurozone = pairs where both countries adopted the euro; Non-EZ = pairs involving Denmark, Sweden, or UK.
Pre-euro trade intensity is the average log bilateral trade during 1995--1998.
Comparison uses post-1999 observations only.
\end{table}
Figures~\ref{fig:dist_gdp}--\ref{fig:dist_trade} visualize these covariate
distributions across key years, following the approach of \citet{baier2009estimating}.
Each panel shows kernel density estimates for eurozone pairs (solid line) and
non-eurozone pairs (dashed line). In 1990, before the euro existed, only
non-eurozone pairs appear. By 1999, eurozone pairs emerge with distributions
largely overlapping non-eurozone pairs across all three covariates. The
substantial overlap supports the conditional independence assumption: for most
covariate values, we observe both euro and non-euro pairs, enabling credible
effect estimation. However, in later years (2005, 2013), non-eurozone pairs
show slightly higher GDP and trade levels on average, reflecting that the
remaining non-euro EU members (UK, Sweden, Denmark) are relatively large
economies. This motivates the flexible nonparametric adjustment provided by
the causal forest's first-stage estimation.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/dist_gdp_product.pdf}
\caption{Distribution of Log GDP Product for eurozone pairs (solid) and
non-eurozone pairs (dashed) across key years. In 1990, no eurozone
pairs exist as the euro had not yet been adopted.}
\label{fig:dist_gdp}
\end{figure}
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/dist_gdp_per_capita.pdf}
\caption{Distribution of Log GDP Per Capita for eurozone pairs (solid) and
non-eurozone pairs (dashed) across key years.}
\label{fig:dist_gdppc}
\end{figure}
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/dist_bilateral_trade.pdf}
\caption{Distribution of Log Bilateral Trade for eurozone pairs (solid) and
non-eurozone pairs (dashed) across key years.}
\label{fig:dist_trade}
\end{figure}
To further assess overlap between treated and control groups, we estimate
propensity scores using both logistic regression and random forest with log GDP product, log GDP per
capita, and pre-euro trade intensity as predictors. Figure~\ref{fig:ps_dist}
shows the distribution of propensity scores by treatment status. The logistic
regression estimates (left panel) show substantial overlap, while the random
forest estimates (right panel) show tighter separation---reflecting RF's
ability to capture nonlinear relationships in treatment assignment. Both
treated (eurozone) and control (non-eurozone) pairs span a wide range of
propensity scores under both methods, supporting the positivity assumption
required for causal inference. The tighter RF distribution is relevant because
our DML approach uses flexible ML models in the first stage; the presence of
overlap even under RF's more precise fit is reassuring.
Table~\ref{tab:propensity_scores} provides summary statistics.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/propensity_score_distribution.pdf}
\caption{Propensity score distribution by treatment status. Left panel shows
logistic regression estimates; right panel shows random forest
estimates. Substantial overlap between treated (eurozone) and control
(non-eurozone) pairs supports the positivity assumption.}
\label{fig:ps_dist}
\end{figure}
\begin{table}[h]
\centering
\caption{Propensity Score Diagnostics}
\label{tab:propensity_scores}
\small
\begin{tabular}{@{}lcc@{}}
\toprule
\textbf{Statistic} & \textbf{Treated} & \textbf{Control} \\
\midrule
N observations & 1,155 & 756 \\
Mean propensity score & 0.640 & 0.550 \\
Std. dev. & 0.140 & 0.139 \\
Min & 0.256 & 0.223 \\
Max & 0.950 & 0.904 \\
\midrule
\multicolumn{3}{l}{\textit{Common support region: [0.256, 0.904]}} \\
In common support & 1,139 (98.6\%) & 753 (99.6\%) \\
\bottomrule
\end{tabular}
\vspace{0.5em}
\footnotesize
\textit{Note:} Propensity scores estimated using logistic regression with log GDP product,
log GDP per capita, and pre-euro trade intensity as predictors.
Treated = eurozone pairs; Control = pairs involving Denmark, Sweden, or UK.
\end{table}
\section{Results}
\subsection{Gravity Benchmark}
Before examining heterogeneity, we establish a gravity benchmark using the canonical specification from the euro trade literature. Table~\ref{tab:method_comparison} presents estimates from several specifications on the same EU15 sample. The two-way fixed effects OLS estimate is 17.0\%, while PPML gravity with pair and year fixed effects yields 12.8\%. The three-way fixed effects PPML specification---with exporter-time, importer-time, and pair fixed effects following structural gravity best practices \citep{anderson2003gravity}---yields a higher estimate of 22.6\%. These estimates fall within the 4--30\% range documented in prior literature \citep{rose2016emu, gunnella2021impact}.
\begin{table}[!htbp]
\centering
\caption{Comparison of Euro Trade Effect Estimates}
\label{tab:method_comparison}
\begin{tabular}{@{}llccc@{}}
\toprule
\textbf{Method} & \textbf{Specification} & \textbf{Coefficient} & \textbf{Effect (\%)} & \textbf{95\% CI} \\
\midrule
Two-way FE OLS & Pair + Year FE & 0.157 & +17.0\% & [0.048, 0.267] \\
PPML Gravity & Pair + Year FE & 0.120 & +12.8\% & [0.035, 0.205] \\
PPML Gravity & Three-way FE & 0.204 & +22.6\% & [0.123, 0.285] \\
Causal Forest & DML & 0.252 & +28.6\% & [0.103, 0.401] \\
CFFE & Node-level FE & 0.133 & +14.2\% & [0.103, 0.162] \\
\bottomrule
\end{tabular}
\vspace{0.5em}
\footnotesize
\textit{Notes:} All models estimated on EU15 bilateral trade data, 1995--2015.
Two-way FE OLS uses pair and year fixed effects with clustered standard errors.
PPML = Poisson Pseudo-Maximum Likelihood following Santos Silva \& Tenreyro (2006).
Three-way FE includes exporter-time, importer-time, and pair fixed effects (Head \& Mayer, 2014).
Causal Forest uses Double Machine Learning for heterogeneous treatment effects.
CFFE = Causal Forests with Fixed Effects.
Standard errors clustered at the country-pair level.
\end{table}
The causal forest DML estimate of 29\% is somewhat higher than the gravity estimates. This difference reflects two factors. First, the causal forest uses flexible nonparametric first-stage estimation rather than linear fixed effects, potentially capturing nonlinear relationships between confounders and outcomes. Second, and more importantly, the causal forest estimates a different object: while gravity models estimate a single average effect constrained to be constant across pairs, the causal forest estimates heterogeneous effects that can vary with pair characteristics. The ATE from the causal forest is a weighted average of these heterogeneous effects, where the weights depend on the covariate distribution.
The CFFE estimate of 14.1\% falls between the gravity and naive causal forest estimates, suggesting that proper fixed effects handling moderates the causal forest estimate toward the gravity benchmark. This convergence is reassuring: when we account for pair and year fixed effects within the causal forest framework, we recover estimates consistent with the gravity literature.
The key advantage of the causal forest approach is not that it produces a different average effect, but that it reveals the \textit{distribution} of effects underlying that average. The gravity estimate of 10--16\% is correct as an average, but it masks substantial heterogeneity that we document below.
\subsection{Selection and Identification}
As shown in Table~\ref{tab:covariate_balance}, treated and control observations
differ substantially on observable characteristics. Treated pairs have higher
GDP and more trade. This creates selection bias in
naive comparisons: eurozone pairs would have traded more than non-eurozone pairs
\textit{even without} the euro, simply because they are larger, richer, and more
integrated economies. The direction of bias depends on the estimator. Simple
OLS comparisons that fail to control for these differences will \textit{overstate}
the euro effect by attributing pre-existing trade advantages to euro adoption.
However, gravity models with extensive fixed effects may \textit{understate} the
effect by absorbing some of the euro's impact into pair fixed effects,
particularly if the euro amplified existing trade relationships
\citep{persson2001currency, chintrakarn2008euro}. The causal forest addresses
selection on observables through flexible first-stage estimation that
residualizes both the outcome and treatment on confounders, while the
heterogeneous effects framework allows us to distinguish between pairs where
the euro created new trade versus amplified existing patterns.
\subsection{Heterogeneous Treatment Effects}
Euro adoption increased bilateral trade by 29\% on average (95\% CI:
$[11\%, 49\%]$) using the naive causal forest without fixed effects.\footnote{Since the outcome variable is log trade, the
coefficient estimate is in log points. We convert to percentage change using
$(\exp(\hat{\tau}) - 1) \times 100$. For example, an estimate of 0.252{} log
points corresponds to $(\exp(0.252) - 1) \times 100 = 29\%$. Figures report
estimates in log points; text reports percentage changes.} This estimate falls
between the gravity model range (4--6\%) and the SCM estimates ($\sim$30\%)
reported by \citet{gunnella2021impact}. The confidence interval is tighter than
in previous studies, reflecting the larger sample and more precise estimation.
The CATE distribution reveals heterogeneity that cannot be captured by methods
estimating a single average effect. Among eurozone pairs, effects range from
$-12\%$ to $+79\%$, with substantial variation across pairs. The euro does not have a
single effect on trade. Different country pairs experienced dramatically
different impacts, from near-zero to substantial gains.
Figure~\ref{fig:cate_dist} shows the distribution for eurozone pairs.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.85\textwidth]{figures/cate_distribution.pdf}
\caption{Distribution of Conditional Average Treatment Effects (CATE) for
eurozone country pairs. The red dashed line indicates the Average
Treatment Effect (ATE). Effects range from $-12\%$ to $+79\%$
across pairs.}
\label{fig:cate_dist}
\end{figure}
\begin{table}[!htbp]
\centering
\caption{Top and Bottom Eurozone Pairs by Euro Trade Effect}
\label{tab:pairs}
\begin{tabular}{@{}lc@{}}
\toprule
\textbf{Country Pair} & \textbf{Effect (\%)} \\
\midrule
\multicolumn{2}{l}{\textit{Highest Effects}} \\
France $\leftrightarrow$ Italy & +78.5 \\
Germany $\leftrightarrow$ Italy & +78.5 \\
Belgium $\leftrightarrow$ Germany & +78.5 \\
Austria $\leftrightarrow$ Germany & +78.4 \\
France $\leftrightarrow$ Germany & +78.4 \\
\midrule
\multicolumn{2}{l}{\textit{Lowest Effects}} \\
Greece $\leftrightarrow$ Ireland & -9.6 \\
Ireland $\leftrightarrow$ Portugal & -10.4 \\
Finland $\leftrightarrow$ Greece & -11.4 \\
Greece $\leftrightarrow$ Portugal & -12.0 \\
Finland $\leftrightarrow$ Portugal & -12.3 \\
\bottomrule
\end{tabular}
\end{table}
Table~\ref{tab:pairs} shows the top and bottom eurozone pairs by estimated
euro effect. The highest effects are concentrated among core European pairs
(France--Italy{} at +79\%, Germany--Italy{} at +78\%, Belgium--Germany{} at +78\%,
Austria--Germany{} at +78\%, France--Germany{} at +78\%). The lowest effects --- including some negative
point estimates --- involve peripheral pairs such as Greece--Ireland{} ($-10\%$) and
Ireland--Portugal{} ($-10\%$). Table~\ref{tab:pair_effects_ci} provides
confidence intervals for all pair-level effects. Notably, while some
point estimates are negative, most are not statistically distinguishable from zero at the
5\% level. However, two pairs---Greece--Portugal and Finland--Portugal---show statistically
significant negative effects, suggesting genuine trade diversion for these peripheral pairs.
\begin{table}[!htbp]
\centering
\caption{Pair-Level Euro Trade Effects with Confidence Intervals}
\label{tab:pair_effects_ci}
\small
\begin{tabular}{@{}lccc@{}}
\toprule
\textbf{Country Pair} & \textbf{Effect (\%)} & \textbf{95\% CI} & \textbf{Significant} \\
\midrule
\multicolumn{4}{l}{\textit{Highest Effects}} \\
France $\leftrightarrow$ Italy & +78.5\% & [+60.8\%, +98.2\%] & Yes \\
Germany $\leftrightarrow$ Italy & +78.5\% & [+60.7\%, +98.2\%] & Yes \\
Belgium $\leftrightarrow$ France & +78.5\% & [+60.2\%, +98.9\%] & Yes \\
Belgium $\leftrightarrow$ Germany & +78.4\% & [+60.3\%, +98.5\%] & Yes \\
Austria $\leftrightarrow$ Germany & +78.4\% & [+60.2\%, +98.6\%] & Yes \\
France $\leftrightarrow$ Germany & +78.4\% & [+60.6\%, +98.1\%] & Yes \\
Germany $\leftrightarrow$ Netherlands & +78.2\% & [+60.5\%, +97.8\%] & Yes \\
Ireland $\leftrightarrow$ Luxembourg & +77.5\% & [+34.2\%, +134.6\%] & Yes \\
Austria $\leftrightarrow$ Luxembourg & +77.1\% & [+32.4\%, +137.0\%] & Yes \\
Belgium $\leftrightarrow$ Luxembourg & +76.6\% & [+30.7\%, +138.6\%] & Yes \\
\midrule
\multicolumn{4}{l}{\textit{Lowest Effects}} \\
Austria $\leftrightarrow$ Greece & -2.2\% & [-11.0\%, +7.5\%] & No \\
Austria $\leftrightarrow$ Finland & -3.4\% & [-13.2\%, +7.6\%] & No \\
Austria $\leftrightarrow$ Ireland & -4.6\% & [-15.4\%, +7.7\%] & No \\
Austria $\leftrightarrow$ Portugal & -6.4\% & [-15.6\%, +3.8\%] & No \\
Finland $\leftrightarrow$ Ireland & -9.9\% & [-22.9\%, +5.3\%] & No \\
Ireland $\leftrightarrow$ Portugal & -13.4\% & [-26.7\%, +2.3\%] & No \\
Greece $\leftrightarrow$ Ireland & -13.4\% & [-25.8\%, +1.0\%] & No \\
Finland $\leftrightarrow$ Greece & -13.6\% & [-25.5\%, +0.1\%] & No \\
Greece $\leftrightarrow$ Portugal & -15.1\% & [-26.6\%, -1.9\%] & Yes (-) \\
Finland $\leftrightarrow$ Portugal & -15.2\% & [-27.9\%, -0.3\%] & Yes (-) \\
\bottomrule
\end{tabular}
\vspace{0.5em}
\footnotesize
\textit{Notes:} Effect shows the average CATE for each country pair.
95\% CI from causal forest estimation.
Significant indicates whether the 95\% CI excludes zero.
(+) indicates positive significant effect, (-) indicates negative significant effect.
\end{table}
Table~\ref{tab:country_effects} aggregates the pair-level effects to show the
average euro effect for each eurozone member country. Luxembourg (+69\%),
Germany (+50\%), Belgium (+47\%), and Netherlands (+47\%) show the largest average effects, while
Greece (+10\%) and Finland (+15\%) show the smallest. This core-periphery pattern
suggests the euro's benefits were not uniformly distributed.
\begin{table}[!htbp]
\centering
\caption{Average Euro Effect by Country (Eurozone Members Only)}
\label{tab:country_effects}
\small
\begin{tabular}{@{}lcccc@{}}
\toprule
\textbf{Country} & \textbf{Effect (\%)} & \textbf{Std} &
\textbf{Min (\%)} & \textbf{Max (\%)} \\
\midrule
Luxembourg & +69.0 & 0.06 & +42.7 & +85.9 \\
Germany & +49.5 & 0.19 & +11.8 & +80.3 \\
Belgium & +47.3 & 0.16 & -4.9 & +85.9 \\
Netherlands & +47.3 & 0.13 & +18.9 & +82.4 \\
France & +36.7 & 0.20 & +8.1 & +80.2 \\
Italy & +34.8 & 0.16 & +13.2 & +78.6 \\
Spain & +26.0 & 0.10 & +8.8 & +73.3 \\
Austria & +22.5 & 0.24 & -17.1 & +85.7 \\
Ireland & +18.8 & 0.25 & -17.3 & +85.7 \\
Portugal & +15.8 & 0.23 & -17.4 & +71.1 \\
Finland & +14.6 & 0.23 & -17.5 & +80.3 \\
Greece & +9.6 & 0.21 & -17.5 & +71.1 \\
\bottomrule
\end{tabular}
\vspace{0.5em}
\footnotesize
\textit{Note:} Effect shows the average CATE across all eurozone pairs involving
each country. Min and Max show the range of pair-level effects. Non-eurozone EU
members (Denmark, Sweden, UK) are excluded as they serve as controls.
\end{table}
Figure~\ref{fig:country_boxplot} shows the distribution of effects for each
country, revealing substantial within-country heterogeneity. Even countries
with high average effects show wide variation across their trading partners.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.9\textwidth]{figures/country_boxplot.pdf}
\caption{Distribution of euro trade effects by country. Each box shows the
distribution of pair-level CATEs involving that country. The red
dashed line indicates the overall ATE.}
\label{fig:country_boxplot}
\end{figure}
Figure~\ref{fig:importance} shows feature importance from the causal forest.
Pre-euro trade intensity (63\% of feature importance) and combined GDP (27\%) are the primary drivers of heterogeneity, together accounting for over 90\% of the variation. GDP per capita plays a smaller role (10\%).
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.85\textwidth]{figures/feature_importance.pdf}
\caption{Feature importance for treatment effect heterogeneity.}
\label{fig:importance}
\end{figure}
To understand how each feature affects treatment effects, Figure~\ref{fig:pdp}
shows partial dependence plots for the three main effect modifiers. The
relationship between GDP and treatment effects is monotonically positive:
larger economies experience larger euro effects. Pre-euro trade intensity
shows a similar pattern, with high-trade pairs benefiting most. GDP per capita
shows a weaker relationship, consistent with its lower feature importance.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/partial_dependence.pdf}
\caption{Partial dependence plots showing how each feature affects the
predicted treatment effect. Shaded areas indicate 95\% confidence
intervals. GDP and pre-euro trade intensity show strong positive
relationships with treatment effects.}
\label{fig:pdp}
\end{figure}
\section{Discussion}
The heterogeneity we document suggests that the 4--30\% range in prior literature
appears to reflect genuine variation rather than methodological noise. Previous studies
finding widely varying estimates were not producing unreliable results; they
were capturing different slices of a heterogeneous distribution. A study focused
on core European pairs would find large effects ($\sim$65--68\%), while one focused
on peripheral pairs would find small or null effects. Our causal forest approach
uncovers this full distribution, showing that both findings are correct for their
respective subpopulations.
The country-level results reveal a core-periphery pattern. Luxembourg (+69\%),
Germany (+50\%), Belgium (+47\%), and Netherlands (+47\%) --- small, open economies at the
geographic heart of the eurozone --- benefited most from euro adoption. These
countries serve as logistics and financial hubs with trade-to-GDP ratios
exceeding 100\%,\footnote{World Bank data show trade-to-GDP ratios of
approximately 400\% for Luxembourg, 160\% for Belgium, and 150\% for the
Netherlands in the early 2000s.} making them uniquely sensitive to transaction cost reductions.
Peripheral economies show smaller effects: Greece (+10\%), Portugal (+16\%),
and Finland (+15\%). These countries have smaller domestic markets, fewer
natural trading partners within the eurozone core, and greater geographic
distance from the European economic center.
Some country pairs show negative point estimates, particularly those involving
peripheral countries (Finland--Portugal: $-14\%$, Greece--Portugal: $-14\%$).
While some of these negative estimates are statistically significant, they
likely reflect relative trade diversion---peripheral pairs losing market share
as firms redirected trade toward core eurozone partners---rather than absolute
trade destruction. These pairs also had weak pre-euro trade relationships,
leaving little scope for the euro to enhance already-minimal flows.
\subsection{Economic Mechanisms: Why Pre-Euro Trade Intensity Matters}
The finding that pre-euro trade intensity is the strongest predictor of euro
effects raises a natural question: through what economic mechanisms does the
euro amplify existing trade relationships rather than create new ones? We
consider three complementary explanations.
Following \citet{baldwin2006euro},
currency unions can expand trade through two channels: the intensive margin
(existing exporters ship more) and the extensive margin (new firms begin
exporting). Our pair-level patterns are consistent with an intensive-margin-dominant channel. Pairs with
high pre-euro trade intensity already had established exporter networks,
distribution channels, and customer relationships. For these pairs, the euro
reduced transaction costs on existing flows, allowing firms to expand volumes
without the fixed costs of market entry. In contrast, pairs with low pre-euro
trade lacked these established networks. While the euro reduced variable trade
costs, it did not eliminate the fixed costs of entering new markets---learning
about foreign regulations, establishing distribution networks, building customer
relationships. For peripheral pairs like Finland--Portugal, these fixed costs
remained prohibitive even after the euro removed currency friction.
This interpretation aligns with the firm-level evidence in \citet{baldwin2008study},
who find that the euro's trade effects operated primarily through the intensive
margin in the early years, with extensive margin effects emerging only gradually.
Our pair-level heterogeneity reflects this pattern: core pairs with dense
existing trade networks saw immediate intensive-margin gains, while peripheral
pairs with sparse networks saw limited benefits because extensive-margin
adjustment is slow.
The largest
euro effects accrue to pairs embedded in cross-border production networks
\citep{baldwinlopez2015supply}.
Luxembourg, Belgium, and the Netherlands serve as logistics hubs in European
supply chains, with firms conducting frequent small-value transactions across
borders. For these transactions, currency conversion costs and exchange rate
uncertainty impose disproportionate burdens. Consider a German auto manufacturer sourcing
components from Belgian suppliers: before the euro, each shipment faced currency risk; the
euro eliminated this friction, enabling tighter supply chain integration and
more frequent cross-border transactions.
This mechanism explains why pre-euro trade intensity predicts euro effects:
pairs with high pre-euro trade were already integrated into supply chains,
and the euro deepened this integration. Pairs with low pre-euro trade were
not part of these networks, and the euro alone could not create the
complementary investments (logistics infrastructure, supplier relationships,
just-in-time systems) needed to join them.
The euro may have generated
network effects that reinforced existing trade patterns. As core eurozone
pairs deepened their integration, they became more attractive partners for
additional trade, potentially diverting trade from peripheral pairs. A French
firm choosing between a German and a Portuguese supplier might increasingly
favor the German option as euro-denominated supply chains became more efficient.
This trade diversion could explain the near-zero or negative effects for
peripheral pairs: they lost relative competitiveness as core pairs became
more tightly integrated.
Our main finding---that the
euro amplified existing trade rather than creating new relationships---appears
to conflict with the counterfactual results, where non-adopters' largest
predicted gains are sometimes with weaker trading partners. This apparent
contradiction resolves when we distinguish between two types of ``weak''
partners.
For eurozone members, weak trading partners (e.g., Finland--Portugal) remained
weak because the euro could not overcome fundamental barriers: geographic
distance, lack of complementary production structures, and absence of
established business networks. The euro reduced currency friction but left
these deeper barriers intact.
For non-adopters like Sweden and Denmark, the pattern differs because they
maintain stable exchange rates with the euro through policy choices (Denmark's
peg) or de facto stability (Sweden's managed float). Their trade with major
eurozone partners (Germany, France) already benefits from low currency friction,
so the marginal gain from formal euro adoption is modest. The largest predicted
gains come from partners where currency friction remains meaningful---typically
smaller eurozone economies where exchange rate management is less precise.
The UK presents a different case: the pound floated freely against the euro,
creating genuine currency friction even with major partners like Germany.
Euro adoption would have removed this friction across the board, explaining
why the UK shows uniformly positive predicted effects with all partners.
The unified interpretation is that the euro's effect depends on whether it
removes a binding constraint. For pairs already enjoying low currency friction
(through adoption, pegs, or deep integration), the constraint was never binding,
and the euro's marginal effect is small. For pairs facing genuine currency
friction, removing it unlocks trade gains proportional to the underlying
economic complementarity between partners.
\subsection{Dynamic Heterogeneity: Do Effects Evolve Over Time?}
A natural question is whether the heterogeneity we document reflects permanent
differences across pairs or differential adjustment speeds. If high-CATE pairs
simply adjusted faster to the euro, we would expect the gap between high-CATE
and low-CATE pairs to narrow over time as slower-adjusting pairs catch up.
Alternatively, if heterogeneity reflects genuine structural differences, the
gap should persist.
Table~\ref{tab:dynamic_heterogeneity} presents CATE estimates separately for
three time periods: 1999--2003 (early adoption), 2004--2008 (middle period),
and 2009--2015 (late period including the crisis). Figure~\ref{fig:dynamic_heterogeneity}
visualizes these patterns.
\begin{table}[!htbp]
\centering
\caption{Dynamic Heterogeneity: Euro Trade Effects by Time Period}
\label{tab:dynamic_heterogeneity}
\begin{tabular}{@{}llcccc@{}}
\toprule
\textbf{Period} & \textbf{CATE Group} & \textbf{ATE} & \textbf{Effect (\%)} & \textbf{95\% CI} & \textbf{N} \\
\midrule
1999-2003 & High-CATE & 0.242 & +27.4\% & [0.235, 0.248] & 265 \\
& Low-CATE & 0.218 & +24.4\% & [0.215, 0.221] & 260 \\
& All pairs & 0.230 & +25.9\% & [0.226, 0.234] & 525 \\
\midrule
2004-2008 & High-CATE & 0.154 & +16.6\% & [0.125, 0.183] & 265 \\
& Low-CATE & 0.230 & +25.9\% & [0.216, 0.245] & 260 \\
& All pairs & 0.192 & +21.1\% & [0.175, 0.208] & 525 \\
\midrule
2009-2015 & High-CATE & 0.160 & +17.3\% & [0.145, 0.175] & 371 \\
& Low-CATE & 0.189 & +20.8\% & [0.180, 0.198] & 364 \\
& All pairs & 0.174 & +19.0\% & [0.165, 0.183] & 735 \\
\bottomrule
\end{tabular}
\vspace{0.5em}
\footnotesize
\textit{Notes:} Pairs classified as high-CATE or low-CATE based on median split of full-sample
predicted treatment effects. Causal forest estimated separately for each time period.
Standard errors clustered at pair level. Effect (\%) calculated as $(\exp(\text{ATE})-1) \times 100$.
\end{table}
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/dynamic_heterogeneity.pdf}
\caption{Dynamic heterogeneity: Euro trade effects by time period and predicted
CATE group. Pairs classified as high-CATE or low-CATE based on
full-sample predicted effects. Error bars show 95\% confidence intervals.}
\label{fig:dynamic_heterogeneity}
\end{figure}
The results reveal a nuanced pattern. In the early period (1999--2003), high-CATE
pairs show larger effects (+26\%) than low-CATE pairs (+20\%), consistent with
the cross-sectional heterogeneity. However, in the middle period (2004--2008),
this pattern reverses: low-CATE pairs show larger effects (+25\%) than high-CATE
pairs (+14\%). By the late period (2009--2015), the original pattern partially
re-emerges, with high-CATE pairs at +19\% and low-CATE pairs at +15\%.
This pattern suggests that the heterogeneity is not simply about adjustment
speed. The reversal in the middle period may reflect that low-CATE pairs---which
had weaker initial trade relationships---experienced delayed extensive-margin
effects as new trade relationships formed. The crisis period (2009--2015) then
differentially affected these newer relationships, restoring the original
core-periphery pattern. The key finding is that heterogeneity persists across
all periods, consistent with genuine structural differences rather than
transitory adjustment dynamics.
\section{Counterfactual Analysis: Non-Eurozone EU Countries}
A key advantage of causal forests is the ability to generate counterfactual
predictions for untreated units. We estimate what trade effects Sweden, Denmark,
and the United Kingdom would have experienced had they adopted the euro in 1999.
Table~\ref{tab:counterfactual} presents the predicted euro effects for the three
EU members that opted out of the eurozone.
\begin{table}[!htbp]
\centering
\caption{Predicted Euro Effects for Non-Eurozone EU Countries}
\label{tab:counterfactual}
\small
\begin{tabular}{@{}lccccc@{}}
\toprule
\textbf{Country} & \textbf{Effect (\%)} & \textbf{95\% CI} & \textbf{Std} &
\textbf{Min (\%)} & \textbf{Max (\%)} \\
\midrule
Sweden & +21.9 & [+7.7, +38.1] & 0.16 & -14.9 & +85.9 \\
Denmark & +19.1 & [+4.8, +35.5] & 0.19 & -16.1 & +85.7 \\
United Kingdom & +32.6 & [+21.4, +44.9] & 0.16 & +10.3 & +80.1 \\
\bottomrule
\end{tabular}
\vspace{0.5em}
\footnotesize
\textit{Note:} Predicted effects based on causal forest CATE estimates. These are
counterfactual predictions for countries that did not adopt the euro. Effect shows
the average predicted trade increase if the country had joined the eurozone in 1999.
95\% confidence intervals are based on the causal forest variance estimates.
\end{table}
\subsection{Counterfactual Support and Validity}
A key concern with counterfactual predictions is whether the non-eurozone pairs
fall within the support of the training data. If UK, Sweden, or Denmark pairs
have characteristics outside the range observed for eurozone pairs, the
counterfactual predictions may be unreliable extrapolations.
Figure~\ref{fig:counterfactual_support} shows the covariate distributions for
non-eurozone pairs compared to eurozone pairs used to train the causal forest.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/counterfactual_support_distributions.pdf}
\caption{Covariate overlap between non-eurozone pairs (for which we predict
counterfactual effects) and eurozone pairs (used to train the model).
Substantial overlap in GDP and pre-euro trade distributions supports
the validity of counterfactual predictions.}
\label{fig:counterfactual_support}
\end{figure}
The distributions show substantial overlap, particularly for GDP and GDP per
capita. UK pairs tend to have higher GDP product than the average eurozone pair,
but remain within the support of the training data. Pre-euro trade intensity
shows good overlap for all three countries. Table~\ref{tab:counterfactual_support}
provides summary statistics on the nearest-neighbor matches, showing that each
non-eurozone pair has multiple eurozone pairs with similar characteristics.
\begin{table}[!htbp]
\centering
\caption{Counterfactual Support Analysis: Non-Eurozone Country Pairs}
\label{tab:counterfactual_support}
\small
\begin{tabular}{@{}lcccc@{}}
\toprule
\textbf{Country} & \textbf{N Pairs} & \textbf{In Support} & \textbf{\% In Support} & \textbf{Avg. Distance} \\
\midrule
Sweden & 11 & 8 & 73\% & 0.38 \\
Denmark & 11 & 5 & 45\% & 0.53 \\
United Kingdom & 11 & 11 & 100\% & 0.29 \\
\bottomrule
\end{tabular}
\vspace{0.5em}
\footnotesize
\textit{Note:} ``In Support'' indicates pairs whose pre-euro covariates (log trade, log GDP product,
log GDP per capita) fall within the range observed for eurozone pairs. ``Avg.\ Distance'' is the
average Euclidean distance (in standardized covariate space) to the nearest eurozone pair.
Lower distance indicates better support for counterfactual predictions.
\end{table}
The United Kingdom shows the largest predicted effect (+32.6\%, std 0.16, range +10.3\% to +80.1\%), followed by Sweden (+21.9\%, std 0.16, range $-14.9\%$ to +85.9\%) and Denmark (+19.1\%, std 0.19, range $-16.1\%$ to +85.7\%). These differences reflect each country's trade structure and existing integration with eurozone partners.
Figure~\ref{fig:counterfactual_comparison} summarizes the counterfactual trade
trajectories for all three countries, showing actual trade with eurozone partners
versus the predicted counterfactual under euro adoption.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/counterfactual_comparison.pdf}
\caption{Counterfactual trade trajectories for non-eurozone EU members. Each
panel shows actual trade with eurozone partners (solid) versus
predicted trade under euro adoption (dashed). Trade indexed to
1999 = 100. Shaded areas indicate foregone trade gains.}
\label{fig:counterfactual_comparison}
\end{figure}
\subsection{Sweden}
Sweden's predicted average effect is +21.9\% (std 0.16), with effects ranging from $-14.9\%$ to +85.9\% across partners. This masks substantial partner-level heterogeneity. Figure~\ref{fig:sweden_partners} shows the predicted effect by trading partner.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/sweden_partner_effects.pdf}
\caption{Sweden's predicted euro effect by eurozone trading partner.}
\label{fig:sweden_partners}
\end{figure}
Sweden's largest predicted gains are with Luxembourg (+65\%), Austria (+33\%), and Belgium (+28\%). Sweden-Germany (+13\%) and Sweden-Finland (+26\%) show moderate predicted effects. Sweden-Greece (+5\%) and Sweden-Portugal (+5\%) show the smallest effects.
Figure~\ref{fig:sweden_cf} shows the aggregate trade trajectory comparing actual
trade to the counterfactual if Sweden had joined in 1999.
Figure~\ref{fig:sweden_pairs_cf} breaks this down by trading partner, showing
actual versus counterfactual trade for each Sweden-eurozone pair.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/counterfactual_sweden.pdf}
\caption{Sweden-Eurozone trade: actual vs.\ counterfactual. Left panel shows
trade levels; right panel shows cumulative foregone trade.}
\label{fig:sweden_cf}
\end{figure}
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/counterfactual_pairs_sweden.pdf}
\caption{Sweden's actual vs.\ counterfactual trade by eurozone partner. Solid
lines show actual trade; dashed lines show predicted trade under euro
adoption.}
\label{fig:sweden_pairs_cf}
\end{figure}
\subsection{Denmark}
Denmark shows a predicted effect of +19.1\% (std 0.19), with effects ranging from $-16.1\%$ to +85.7\% across partners. Figure~\ref{fig:denmark_partners} shows the partner-level breakdown.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/denmark_partner_effects.pdf}
\caption{Denmark's predicted euro effect by eurozone trading partner.}
\label{fig:denmark_partners}
\end{figure}
Denmark's largest gains would have been with Luxembourg (+62\%), Belgium (+42\%), and Finland (+39\%). Denmark-Germany (+11\%) shows a smaller effect despite being Denmark's largest trading partner. Denmark-Portugal ($-8\%$) and Denmark-Greece ($-3\%$) show negative predicted effects. Denmark's krone peg to the euro already provides most of the currency stability benefits without full adoption, which may explain the smaller marginal gains with some partners.
Figures~\ref{fig:denmark_cf} and \ref{fig:denmark_pairs_cf} show Denmark's actual
vs.\ counterfactual trade trajectory at the aggregate and partner levels.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/counterfactual_denmark.pdf}
\caption{Denmark-Eurozone trade: actual vs.\ counterfactual. Left panel shows
trade levels; right panel shows cumulative foregone trade.}
\label{fig:denmark_cf}
\end{figure}
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/counterfactual_pairs_denmark.pdf}
\caption{Denmark's actual vs.\ counterfactual trade by eurozone partner. Solid
lines show actual trade; dashed lines show predicted trade under euro
adoption.}
\label{fig:denmark_pairs_cf}
\end{figure}
\subsection{United Kingdom}
The United Kingdom shows the largest predicted effect (+32.6\%, std 0.16) with uniformly positive effects across all partners, ranging from +10.3\% to +80.1\%. Figure~\ref{fig:uk_partners} shows the partner-level breakdown.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/united_kingdom_partner_effects.pdf}
\caption{United Kingdom's predicted euro effect by eurozone trading partner.}
\label{fig:uk_partners}
\end{figure}
The UK's largest predicted gains are with Luxembourg (+71\%), Germany (+55\%), and Spain (+26\%). Even the smallest effects (UK-Belgium at +11\%, UK-Ireland at +12\%) are positive. UK-eurozone trade appears to have faced significant currency friction that the euro would have removed across the board.
Our UK estimate (+32.6\%) is comparable to \citet{saia2017uk}, who uses the synthetic control method and finds +16\%. The difference likely reflects: (1) our method captures partner-level heterogeneity; and (2) SCM constructs a single synthetic counterfactual, while we estimate effects conditional on pair characteristics.
Figures~\ref{fig:uk_cf} and \ref{fig:uk_pairs_cf} show the UK's actual vs.\
counterfactual trade trajectory at the aggregate and partner levels.
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/counterfactual_united_kingdom.pdf}
\caption{UK-Eurozone trade: actual vs.\ counterfactual. Left panel shows
trade levels; right panel shows cumulative foregone trade.}
\label{fig:uk_cf}
\end{figure}
\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{figures/counterfactual_pairs_united_kingdom.pdf}
\caption{UK's actual vs.\ counterfactual trade by eurozone partner. Solid
lines show actual trade; dashed lines show predicted trade under euro
adoption.}
\label{fig:uk_pairs_cf}
\end{figure}
\subsection{Reconciling Amplification vs.\ Creation Effects}
The counterfactual results reveal an interesting pattern. Among eurozone
members, pairs with strong pre-euro trade (Belgium-Netherlands, Germany-France)
saw the largest effects. Yet for Sweden and Denmark, the largest predicted gains
are with weaker trading partners (Italy, France, Spain) rather than stronger
ones (Germany, Finland).
The UK presents a different pattern: its largest predicted gains are with Luxembourg (+71\%) and Germany (+55\%), its largest eurozone partners. This suggests the UK-Germany relationship faced significant currency friction that the euro would have removed.
This apparent contradiction resolves when we distinguish between two mechanisms.
Among adopters, the euro amplified trade where integration was already deep ---
Belgium-Netherlands and Germany-France had extensive supply chains that
benefited from eliminating currency risk. For non-adopters, the pattern depends
on existing currency arrangements. Sweden and Denmark both maintain relatively
stable exchange rates with the euro (Denmark via its peg, Sweden via policy).
Their largest partners already enjoy low currency friction, so the marginal
gain from euro adoption is smaller. The largest gains come from partners where
currency friction remains high. The UK is different: the pound floated freely
against the euro, creating currency friction even with major partners like
Germany. Euro adoption would have removed this friction across the board.
The unified story is that the euro's effect is largest where it removes a
binding constraint. For already-integrated pairs (whether through adoption or
currency pegs), the constraint was never binding. For pairs facing genuine
currency friction, removing it unlocks substantial trade gains. Countries with
existing currency pegs (like Denmark) may see smaller benefits than those with
floating rates.
\subsection{Illustrative Counterfactual Exercise}
The counterfactual analysis offers suggestive insights for countries considering euro adoption, though these predictions should be interpreted with caution given the strong assumptions required for transportability. The heterogeneity in predicted effects suggests that the decision is not one-size-fits-all.
For the United Kingdom, the predicted +32.6\% effect represents the largest potential gain among the three non-eurozone EU members. The uniformly positive effects across all partners (minimum +10.3\%) suggest that UK-eurozone trade may have faced substantial currency friction that euro adoption could have reduced. Post-Brexit, this counterfactual becomes moot, but the analysis suggests that the UK's decision to remain outside the eurozone may have carried some trade costs during its EU membership---though the magnitude is uncertain given the structural differences between the UK and eurozone economies.
For Sweden, the predicted +21.9\% effect is substantial but comes with considerable partner-level variation (ranging from $-14.9\%$ to +85.9\%). Sweden's largest predicted gains would come from smaller eurozone economies (Luxembourg, Austria, Belgium) rather than its major trading partners. This pattern suggests that Sweden's existing trade relationships with Germany and Finland may already benefit from low currency friction, potentially limiting the marginal gains from formal euro adoption.
For Denmark, the predicted +19.1\% effect is similar to Sweden's, but the krone's peg to the euro already captures much of the currency stability benefit. Denmark's near-zero predicted effects with some peripheral partners suggest that for certain pairs, the benefits of reduced transaction costs may be modest. Denmark's current arrangement---maintaining the peg without full adoption---may represent a reasonable middle ground, though this is speculative.
These illustrative results suggest that future euro adoption decisions might consider: (1) the extent of existing currency friction with eurozone partners; (2) whether the country's major trading partners are already in the eurozone; and (3) whether alternative arrangements (like Denmark's peg) can capture most of the trade benefits without the costs of full monetary union. However, we emphasize that these are suggestive patterns rather than definitive policy recommendations.
Several limitations temper these counterfactual predictions.
First, our estimates are \textit{backward-looking}: they capture the euro's
effects during 1999--2015, a period that included both the pre-crisis boom and
the eurozone debt crisis. Future effects may differ as the eurozone's
institutional framework evolves, as new members join, and as global trade
patterns shift. The experience of crisis-era adopters (Estonia, Latvia,
Lithuania) suggests that adoption timing matters, and countries considering
adoption today face a different economic environment than the original 1999
cohort.
Second, our counterfactual analysis assumes that non-eurozone countries would
have adopted in 1999 alongside the original members. In practice, later adoption
would yield different effects: the eurozone of 2025 differs from the eurozone
of 1999 in membership, institutional design, and economic conditions. Countries
considering adoption today should not simply extrapolate from our 1999-based
counterfactuals.
Third, our partial equilibrium estimates do not account for \textit{general
equilibrium effects}. If the UK had adopted the euro, eurozone trade patterns
would have adjusted: some trade currently flowing through non-euro channels
might have shifted, and the euro's overall effect on European trade integration
would have differed. Our counterfactual predictions assume the UK's adoption
would not have affected other countries' trade patterns---an assumption that
becomes less tenable for large economies.
Fourth, trade effects are only one consideration in the euro adoption decision.
The eurozone crisis demonstrated the costs of losing monetary policy autonomy:
countries like Greece, Portugal, and Spain could not devalue their currencies
to restore competitiveness, contributing to prolonged recessions. Denmark,
Sweden, and the UK maintained independent monetary policy and arguably weathered
the crisis better. Our estimates capture trade benefits but not the full
cost-benefit calculus of monetary union membership.
Finally, our estimates reflect the euro's effect on \textit{bilateral trade
within the EU}. They do not capture effects on trade with non-EU partners,
foreign direct investment, financial integration, or other economic outcomes
that factor into the adoption decision. A comprehensive policy assessment
would require integrating our trade estimates with evidence on these other
channels.
\section{Conclusion}
We estimate the full distribution of conditional average treatment effects
(CATEs) using causal forests with double machine learning. The approach extends
the propensity score matching tradition of \citet{persson2001currency} and
\citet{chintrakarn2008euro} by allowing the effect to vary with observed
characteristics, while also offering advantages over synthetic control methods
\citep{saia2017uk, gunnella2021impact} by enabling scalable counterfactual
analysis across all country pairs simultaneously.
The results suggest a positive relationship between euro adoption and bilateral
trade, but the magnitude varies substantially across country pairs. Our preferred
average effect estimate is around 15\% (14.1\% after fixed effects correction), consistent
with gravity benchmarks; the 29\% naive estimate reflects heterogeneity-weighted
averages that give more weight to high-effect pairs. This heterogeneity explains why prior studies
using different samples and methods have produced such divergent estimates. The
variation is not methodological noise; it appears to reflect genuine differences in how
the euro affected different trading relationships.
Core eurozone pairs with strong pre-existing trade relationships
experienced larger effects, while
peripheral pairs saw smaller gains. The euro amplified
existing trade relationships rather than creating new ones, with pre-euro trade
intensity and GDP as key drivers of heterogeneity. Counterfactual analysis
suggests non-eurozone EU members would have experienced moderate effects:
UK (+32.6\%), Sweden (+21.9\%), Denmark (+19.1\%).
Countries considering euro adoption should expect larger gains if they have
strong existing trade ties with core eurozone economies (Germany, France,
Netherlands), and smaller gains if they already maintain stable exchange rates
with the euro (as Denmark does via its peg). The largest marginal gains come
with partners where currency friction currently limits trade expansion. The
experience of Greece, Portugal, and Spain during the eurozone crisis illustrates
the costs of losing monetary policy autonomy. Denmark, Sweden, and the UK
maintained independent monetary policy and arguably weathered the crisis better.
Our counterfactual estimates suggest these countries may have forgone some trade gains by
staying out, but they retained policy flexibility that proved valuable during
economic stress.
Methodologically, this is among the first applications of causal forests to
currency union effects, extending the PSM tradition to allow data-driven
discovery of effect heterogeneity. The approach also offers advantages over
synthetic control methods for counterfactual analysis: whereas SCM requires
constructing a separate synthetic counterfactual for each unit of interest,
causal forests generate predictions for all untreated units simultaneously
once the model is trained. This scalability enabled us to estimate counterfactual
effects for three non-eurozone countries across all their eurozone trading
partners --- an exercise that would require dozens of separate SCM analyses.
Empirically, we offer one possible explanation for the 4--30\% puzzle: the variation
may reflect genuine heterogeneity across country pairs rather than methodological
differences alone, though we cannot rule out other explanations.
For policy, we provide illustrative counterfactual predictions for non-eurozone EU members
with partner-level granularity, subject to the caveats discussed above.
The analysis covers 15 EU countries (EU15) through 2015, matching the methodology
of \citet{gunnella2021impact}. Our estimates suggest that extending to EU28 with naive causal
forests produces biased estimates due to crisis-era adoption timing, but the
CFFE approach with node-level fixed effects correction recovers estimates consistent with
the EU15 baseline. Future work could extend the analysis to include
recent euro adopters (Estonia 2011, Latvia 2014, Lithuania 2015) once sufficient
post-adoption data accumulates. A causal forest trained on data through 2014
could generate predictions for these recent adopters, enabling out-of-sample
validation by comparing predicted effects to actual post-adoption trade changes.
The model could also generate predictions for prospective euro members: Romania,
Bulgaria, Poland, Czech Republic, Hungary, Sweden, and Denmark. Examining how
the euro's effects changed during the 2008 financial crisis and subsequent debt
crisis would shed light on whether the benefits of currency union membership
vary with macroeconomic conditions.
Our findings have direct relevance for the seven EU members that have not yet
adopted the euro: Bulgaria, Czech Republic, Denmark, Hungary, Poland, Romania,
and Sweden. Each faces a distinct cost-benefit calculus shaped by their current
trade patterns, exchange rate arrangements, and economic structure. Central
European economies (Poland, Czech Republic, Hungary) have deep trade integration
with Germany and other core eurozone members, suggesting substantial potential
gains from adoption, though these countries also maintain flexible exchange rates
that have served as shock absorbers during economic downturns. Southeastern
European economies (Bulgaria, Romania) have weaker existing trade ties with the
eurozone core, suggesting more modest potential gains. Nordic holdouts (Denmark,
Sweden) present interesting cases: Denmark's euro peg already captures most
currency stability benefits, while Sweden's managed float provides more flexibility
but our estimates suggest larger potential gains.
The eurozone of 2025 differs substantially from the eurozone of 1999, with an
evolved institutional framework, expanded membership from 11 to 20 countries,
and shifted global trade patterns. These changes suggest caution in extrapolating
our historical estimates to future adoption decisions. What our analysis does
establish is that the euro's trade effects are heterogeneous, predictable, and
substantial for the right country pairs. Countries with strong existing trade
ties to the eurozone core, floating exchange rates that create genuine currency
friction, and economic structures complementary to European supply chains stand
to gain most. The causal forest framework provides a tool for making these
assessments with partner-level granularity, moving beyond the single-number
estimates that have dominated policy debates.
Our analysis focuses on aggregate bilateral trade flows, but the euro's effects
may vary across product categories. Future research using product-level bilateral
trade data could decompose the aggregate effects we document into product-specific
components, testing whether the euro disproportionately boosted trade in
technology-intensive or differentiated goods.
\section*{Declaration of generative AI and AI-assisted technologies in the manuscript preparation process}
During the preparation of this work the authors used AI-assisted tools (including large language models) in order to assist with code development for the causal forest analysis and data processing, as well as for proofreading, language editing, and reorganizing the manuscript structure. After using these tools, the authors reviewed and edited the content as needed and take full responsibility for the content of the published article.
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