is precisely what we want for the purposes of constructing synthetic control firms, namely we would like some very large importing firms that are not participants and some firms that trade the same goods as the treated firm. The SCM uses data from non-IHC firms to construct a synthetic control firm that looks like an IHC firm, but that is possible only if the non-IHC firms demonstrate enough variation in their characteristics that they are capable of reproducing the IHC firms in terms of import composition and dynamics.

**<u>Table 5.  Annual Import Values in 2010 for IHC and Non-IHC Firms</u>**

||Distrib<br>|ution of firm i<br>|mport values in 2<br>|010 in Serbian<br>|Dinars<br>||
|---|---|---|---|---|---|---|
||Mean|Median|Standard<br>deviation|Minimum|Maximum|Number<br>of firms|
|IHC firms by the end|||||||
|of 2013|1,354 million|654 million|1,656 million|53 million|6,013 million|32|
|Non-IHC firms by the<br>end of 2013|49 million|2.7 million|881 million|50|93,633 million|22,485|
|All firms|51 million|2.7 million|884 million|50|93,633 million|22,517|
|Ratio IHC/Non-IHC|27|244|1.88|1.1 million|0.06||

Source: Authors’ calculations based on Serbian customs data.

# **4.3 Implementation Details**

In Section 3 we described the SCM in abstract terms. In practice our application of the SCM faced a number of challenges. We describe here briefly the details of implementation.<sup>38</sup> The primary challenge for estimation was that even the smoothed outcome variables exhibit a high degree of volatility. A different issue (with related implications) is that we use a relatively large number of conditioning variables, especially with respect to the composition of imports.<sup>39</sup> These two features of our analysis mean that we require substantially larger donor pools than is typical in SCM studies, because smaller donor pools were unable to successfully construct the synthetic

> 38 We perform our estimation using the _synth_ routine for STATA developed by Abadie et al. (2010) and use the full nesting procedure to determine the **_V_** matrix.  The procedure identifies through a regression the relative predictive power of the k covariates in the vector Z for the outcome variable and assigns larger weights to covariates with larger predictive power.  The procedure takes those weights as initial values for the importance of each covariate and then iterates until optimal weights V* and W* are obtained. The method iterates between solving for the V* matrix and the W* matrix until it reaches an optimal solution.  In our case we limit the number of iterations between V and W matrices to 50 in order to achieve a solution in a reasonable period of time.

> 39 We could simplify the analysis considerably by aggregating commodities into even larger bundles: primary products and manufactured goods, for example.  This would give the estimator fewer targets to hit and so imply a better statistical fit.  But more aggregation gives less confidence that the synthetic control firm constructed by the SCM procedure offers a meaningful counterfactual.  This is a trade-off but we err on the side of less aggregation in order to allow matching of synthetic control and treated firm at the level of broad import bundles.

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