## Abstract

This paper investigates the relationship between international trade and migration with the specific aim of estimating direct and indirect effect of the latter on cross-border flows of both homogeneous and differentiated goods. Adopting a spatial econometric approach along with a gravity model set-up, we account for the role of ethnic communities in neighbouring countries on trade, and we propose a new way to define neighbours based on the intensity of links in the migration network. Our approach is particularly well suited to measure the indirect effect stemming from the presence of significant ethnic communities on trade through a “market familiarization” effect. Using data covering all countries between 1970 and 2000, we find a significant indirect effect of migration on trade, that depends on the chosen weight matrix.

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## Notes

- 1.
Although subsequent work has shown that the actual magnitude of this pro-trade effect is smaller than originally estimated (see Felbermayr et al. 2010), its existence and its specific importance for differentiated goods has always been confirmed.

- 2.
- 3.
In this context a spatial spillover is defined as the relationship between a characteristic of a country and the outcome of another country located in its neighbourhood (LeSage 2014).

- 4.
The exact meaning of

*significant number*of migrants is explained in Sect. 2.1. - 5.
Similarly, one could let

*k*be a migration neighbour of the destination country*j*. In such a case migrants from*i*to*k*should represents another indirect channel affecting trade from*i*to*j*. However, we have no theoretical and empirical reason to model this second type of network dependence. - 6.
Second-generation Albanians also play a role, since some of the Italian migrants abroad can have family ties to Albania.

- 7.
Also Anselin and Arribas-Bel (2013) demonstrated by simulation experiments that fixed effects correctly remove autocorrelation only in some specific cases.

- 8.
Assuming two countries,

*i*and*h*, let \(N_i\) be the total number of migrants from country*i*, \(N_h\) the total number of migrants to country*h*, \(N_k\) the overall total number of migrants and \(N_{ih}\) the observed number of migrants from*i*to*h*. Under the null hypothesis of random co-occurrence, i.e. country*h*hosts indifferently migrants from every origin country, the probability of observing*X*migrants is given by the hypergeometric distribution$$\begin{aligned} H(X|N_k,N_i,N_h) = \frac{{N_i \atopwithdelims ()X} {{N_k-N_i} \atopwithdelims (){N_h-X}}}{{N_k \atopwithdelims ()N_h}} \end{aligned}$$and we can associate a

*p*value with the observed \(N_{ih}\) as$$\begin{aligned} p(N_{ih}) = 1 - \sum _{X=0}^{N_{ih}-1} H(X|N_k,N_i,N_h). \end{aligned}$$ - 9.
The share of links present in both networks has grown from 65% in 1960 to more than 70% in 2000. Sgrignoli et al. (2015) provides evidence pointing in the same direction.

- 10.
More in details, since we also need to account for the time index in the pooled model specification (see Sect. 3) the matrix that defines the set of our origin countries’ neighbours has dimension \(n^2*t \times n^2*t\) and it is constructed as follows: \(\mathbf W ^{M}_{Kr,t} = I_t \otimes \mathbf W ^M_{Kr}\), where \(\mathbf W ^M_{Kr} = \mathbf W ^M \otimes I_n\).

- 11.
All the data (except for the dummies) are in \(\log _{10}\).

- 12.
To compute direct and indirect impacts in the SDM specification for the

*r*th explanatory variable, we compute the following partial derivative expression: \(\frac{\partial \mathbf T _{ij}}{\partial \mathbf X _{k,hk}} = S_{r}(\mathbf W ^{M}_{Kr})_{ij,hk} , \forall k = 1,\ldots , K\), where \(S_r (\mathbf W ^{M}_{Kr}) = V(\mathbf W ^{M}_{Kr}) (I_{n^2} \beta _k + \mathbf W ^{M}_{Kr} \gamma _k)\) is a \(n^2 \times n^2\) matrix, with \(V(\mathbf W ^{M}_{Kr}) = (I_{n^2} - \rho \mathbf W ^{M}_{Kr})^{-1}\). The presence of global spillovers can be seen by recognizing that \((I_{n^2} - \rho \mathbf W ^{M}_{Kr})^{-1} = I_{n^2} + \rho \mathbf W ^{M}_{Kr} + \rho ^2 \mathbf W ^{M,2}_{Kr} + \ldots\) For each explanatory variable in the model, the direct impact is the average of the values in the main diagonal of \(S_r(\mathbf W ^{M}_{Kr})\), while the total impact is determined as the sum of all the elements of the matrix, divided by \(n^2\). The indirect impact is simply the difference between the total and the direct effect: \(Indirect = Total - Direct = \frac{\sum _{ij}\sum _{hk}(S_r(\mathbf W ^{M}_{Kr}))_{ij,hk}}{n^2} - \frac{\sum _{ij}\sum _{hk} diag(S_r(\mathbf W ^{M}_{Kr})_{ij,hk})}{n^2}\). - 13.
We use nominal values for trade data, as well as for GDP per capita. Besides being customary in the literature [see for instance Head et al. (2010)], the choice is motivated by the fact that price levels are part of the multilateral trade resistance term: hence, by properly taking into account the MTR, there is no need for any additional deflation.

- 14.
Santos Silva and Tenreyro (2006) warn against the use of log-linearized gravity models, because of the loss of information associated with discarding country-pairs with zero trade flows. For this reason, we have also performed a Poisson pseudo maximum likelihood (PPML) estimation: we find that both OLS and PPML yield a significant effect of migration on trade.

- 15.
Table 8 in the Appendix reports the standard errors from a one-way clustering approach on country pairs to control for auto-correlation and heteroskedasticity. The two different alternatives for correcting standard errors yield qualitatively similar results in terms of significance of the coefficients.

- 16.
This is in good agreement with the literature [see for instance Felbermayr et al. (2015)] and suggests that distance picks up the effect of formal and informal knowledge barriers.

- 17.
The estimation approach proposed in Kelejian and Piras (2014) to remove endogeneity applies only to SAR models.

- 18.
It obviously follows that in the spatial autoregressive models we do not include origin- and destination- fixed effects.

- 19.
\(\mathbf W ^{M}_{Kr,t}\), which is the \(n^2*t \times n^2*t\) network weight matrix described in Sect. 2.1, constructed on 1960 migration data, and therefore a time invariant matrix where data for 1960 is replicated t=4 times.

- 20.
The spatial weight matrix is computed as the inverse distance metric (1 /

*dist*). We call this matrix \(\mathbf W ^{S}_{Kr,t}\), that is a \(n^2*t \times n^2*t\) matrix generated using a Kronecker product on a initial \(n * n\) inverse distance weight matrix. - 21.
In order to make our work comparable with Behrens et al. (2012), who found this parameter to be negative in the Cliff–Ord (SARAR) specification, we also estimated that same model, finding a negative \(\rho\) coefficient as well. SARAR regression results are available upon request.

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## Appendix

### Appendix

See Table 8.

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Metulini, R., Sgrignoli, P., Schiavo, S. *et al.* The network of migrants and international trade.
*Econ Polit* **35, **763–787 (2018). https://doi.org/10.1007/s40888-018-0106-6

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### Keywords

- Trade
- Migration
- Gravity model
- Spatial econometrics
- Networks

### JEL Classification

- F14
- F22
- C21