2.1 Overview of the Methodology

We use the synthetic control method (Abadie and Gardeazabal, Reference Abadie and Gardeazabal2003; Abadie et al., Reference Abadie, Diamond and Hainmueller2010, Reference Abadie, Diamond and Hainmueller2015) to construct a no-war counterfactual for monthly Russian imports.Footnote ⁶ The synthetic control method is a statistical tool used to estimate the causal impact of a treatment or intervention – in our case, the war and the following sanctions. The gist of the synthetic control method lies in its ability to create an artificial comparison term that is as similar as possible to the unit receiving the treatment, allowing researchers to make causal inferences even in non-experimental settings. More formally, the synthetic control method provides a data-driven procedure to construct a robust counterfactual from a weighted average of eligible control units.

Gravity models represent a workhorse tool for trade economists (Head and Mayer, Reference Head, Mayer, Gopinath, Helpman and Rogoff2014), also for the analysis of trade shocks. However, for specific research designs, the features of the synthetic control method might be more suitable. For instance, in the case of endogenous trade policy shocks, such as the war and following sanctions, the gravity coefficients might be highly sensitive to the chosen sample, which can be concerning when choosing a proper counterfactual (Saia, Reference Saia2017). Without a proper exogenous shock, a standard gravity model may represent “a regression of endogenous variables on endogenous variables” (De Benedictis and Taglioni, Reference De Benedictis, Taglioni, De Benedictis and Salvatici2011). Unlike a standard gravity framework, the synthetic control method may alleviate concern related to non-random assignment of the treatment (Saia, Reference Saia2017) and the presence of time-varying heterogeneity (Xu, Reference Xu2017).

In addition to the above issues related to the research design, the synthetic control method yields an immediate, time-varying, and easy-to-interpret measurement of the overall effect of a policy change, where a gravity equation provides a coefficient, indicating its partial effect (Addessi et al., Reference Addessi, Biagi and Brandano2019). Furthermore, a static gravity framework may fail to capture a time-varying impact. As we show in Section 4, the average effect of the war and related sanctions on exports to Russia is far from the actual time-varying value. For all these reasons, the synthetic control methodology has been used widely in the international trade literature (e.g., Billmeier and Nannicini, Reference Billmeier and Nannicini2013; Saia, Reference Saia2017; Breinlich et al., Reference Breinlich, Leromain, Novy and Sampson2020; Douch and Edwards, Reference Douch and Edwards2022; Adarov, Reference Adarov2023) and to analyze the effects of sanctions on GDP (Gharehgozli, Reference Gharehgozli2017).

In our setting, the war and the following sanctions represent the treatment, whereas the treated units are merchandise exports to Russia from each partner. For such trade flows, the synthetic control method builds a corresponding hypothetical no-war counterfactual, derived from a weighted average of third countries’ imports from the same partner. The above weights minimize the distance between the counterfactual exports and the observed ones before the war. In other words, the objective is to find a combination of export flows that may accurately track the targeted export flow before the war. Hence, after the treatment, one may carry over time such weights and use the untreated flows to compute the no-war hypothetical Russian imports from the given partner.

When aggregated, these distinct counterfactual imports constitute the total exports to Russia that would have been observed in a no-war scenario. At each point in time, the total effect of the war and following sanctions on Russian imports is the wedge between the observed Russian imports and their respective counterfactual. Notice that we can use this bottom-up approach also to disentangle the evolution of exports from distinct groups of countries (e.g., sanctioning vs. non-sanctioning countries), or for specific sectors, as we compute a counterfactual for each aggregate and sectoral trade flow to Russia.

2.2 Building the Counterfactual

We consider exports from country i to Russia, X _i→Russia as the treated unit. For such trade flow, there are J ⁱ untreated trade flows that can be used to construct the counterfactual. In line with the literature (e.g., Head and Mayer, Reference Head, Mayer, Gopinath, Helpman and Rogoff2014; Saia, Reference Saia2017), we assume that the exports from country i to j are some function of k predictors, Z^i→j = Z _1,i→j, …, Z _k,i→j. We denote as Zⁱ the k × J ⁱ-dimensional matrix of predictors of untreated trade flows originating from country i to the J ⁱ destinations. By analogy, Z ^i→Russia represents the vector of predictors of the trade flows from country i to Russia. Let T ₀ = 2022M02 represent the starting time of the war.

We are interested in obtaining the effect of war and sanctions on trade flows to Russia, τ _i→Russia,t, at time t, i.e.,

(1)$$\tau _{i\to Russia, t} = X_{i\to Russia, t}^W -X_{i\to Russia, t}^{NW} $$

for t > T ₀, where $X_{i\to Russia, t}^W $ are the exports from i to Russia under war at time t and $X_{i\to Russia, t}^{NW} $ are the exports from i to Russia at time t under no war. It follows that the observed trade exports to Russia correspond to the war scenario, i.e., $X_{i\to Russia, t} = X_{i\to Russia, t}^W $ for t > T ₀. Hence, to obtain τ _i→Russia,t, we need to compute $X_{i\to Russia, t}^{NW} $. Given a set of appropriately chosen weights, $X_{i\to Russia, t}^{NW} $ is given by

(2)$$\hat{X}_{i\to Russia, t}^{NW} = \mathop \sum \limits_{\,j = 1}^{J^I} w_{i, j}X_{i\to j, t}$$

where w _i,j represents the weight for the jth untreated export from i to j, with w _i,j ∈ [0, 1] and $\sum\nolimits_j {w_{i, j} = 1} $. It follows that the synthetic counterpart for τ _i→Russia,t is given by

(3)$$\hat{\tau }_{i\to Russia, t}^{NW} = X_{i\to Russia, t}^W -\hat{X}_{i\to Russia, t}^{NW} $$

Let v_i = (v _i,1, …, v _i,k) denote a set of weights assigned to each of the k for the flows originating from country i. The problem of finding the optimal weights w _i,j and v_i can then be written as

(4)$$\eqalign{& \mathop {\min }\limits_{( {{\vector \bf w}^i, {\vector V}^i} ) } ( {{\boldsymbol Z}^{i\to Russia}-{\bf \vector w}^i{\boldsymbol Z}^i} ) ^{\prime}{\bf \vector V}^i( {{\boldsymbol Z}^{i\to Russia}-{\vector \bf w}^i{\boldsymbol Z}^i} ) \cr & {\rm s}.{\rm to}\,{\boldsymbol w}^i\in [ {0, \;1} ] ^J\,{\rm and}\,\mathop \sum \limits_{\,j = 1}^{J^i} w_{i, j} = 1} $$

where ${\bf \vector V}^i$ represents a k-dimensional diagonal matrix obtained from the k-dimensional vector v_i, and ${\bf \vector w}^i$ represents a J ⁱ-dimensional vector of weights w _i,j.

To obtain $\hat{X}_{i\to Russia, t}$, we repeat the described procedure for all origin countries i′ for which exports to Russia and other $J^{{i}^{\prime}}$ destinations are available. By aggregating over all origins i, we obtain the counterfactual total exports to Russia, $\hat{X}_{\to Russia, \;t}^{NW} $, as

(5)$$\hat{X}_{\to Russia, \;t}^{NW} = \mathop \sum \limits_i \hat{X}_{i\to Russia, t}$$

Our design also helps us delve into sectoral trade flows to assess the impact of the war and the following sanctions on specific goods (e.g., high-tech items exports). To this end, for the sector-level analysis, we run an ad-hoc synthetic control calibration that features industry-level predictors in the Zⁱ matrix, and compute the weights needed to obtain the counterfactual sectoral exports to Russia. We detail the data used in the analysis in Section 3.