returns of neighboring countries within the spatial system. In other words, incorporating the spatial interaction effects helps understand the nature and magnitude of spillover effects across countries. To illustrate the spatial spillovers implied by the estimates of the model, consider equation (1) rewritten as: Then, recursive substitution shows that the effect _h_ -periods ahead of a one-time shock to _Vt_ is<sup>_∂_</sup> _∂V_<sup>_<u>gt</u>_</sup><sup><u>+</u></sup> _t_<sup>_<u>h</u>_= [(</sup><sup>_I −ρW_)</sup><sup>_−_1(</sup><sup>_βI_+</sup><sup>_λW_)]</sup><sup>_h_(</sup><sup>_I −ρW_)</sup><sup>_−_1.The short-run effect is just</sup> _∂V_<sup>_<u>∂gt</u>_</sup> _t_<sup>= (</sup><sup>_I −_</sup> _ρW_ )<sup>_−_1</sup> . Hence the contemporaneous impact of a shock hitting a particular country (i.e., a shock to a particular element of _Vt_ ) diminishes with distance at a rate that depends on the elements of the weight matrix _W_ and the spatial coefficient _ρ_ . It also declines over time at a rate that depends on _β, λ_ and _ρ_ . The larger (in absolute value) these parameters, the larger the eigenvalues of the transition matrix [( _I − ρW_ )<sup>_−_1</sup> ( _βI_ + _λW_ )], and the more persistent the effects of the shock.

For illustration, Figure 3 reports the impact on selected countries of one-time shocks to equity returns in the U.S., the U.K., Germany, Argentina and Turkey. The graphs on the left side of the figure show the responses obtained with the full-sample estimates using the FDI spatial weight matrix, and the graphs on the right side show the responses when using instead the bilateral trade weight matrix. In each case, the graphs show the contemporaneous response to a unit shock to equity returns, and the dynamics over the subsequent three quarters.<sup>23</sup> – Two general features are worth noting. First, convergence is quite fast after just four quarters, the impacts arising from the FDI linkages have virtually vanished; with the trade linkages, they vanish even faster. The reason is that the eigenvalues of the transition matrix turn out to be fairly small in absolute value (under 0.30), thus implying little persistence. Second, convergence is monotonic with the FDI matrix, but oscillating with the trade matrix. This is due to the larger negative estimate of the space-time lag in the latter specification.

The short-run effects are, in some cases, fairly substantial. For example, a unit shock to U.S. returns raises Mexican returns by 0.35 percent under the FDI specification of the weight matrix, and by a whopping 2.5 percent under the bilateral trade specification. In the latter case, U.S. shocks also have a larger impact on equity returns in Brazil and Argentina. Likewise, the impact of shocks to German stock returns on other countries is much larger under the bilateral trade specification of the weight matrix than under the FDI specification. The reason for these differences is twofold. First, the estimate of the contemporaneous spatial effect is almost twice as large under the former specification than under the latter. Second, the bilateral trade links of the countries shown with the U.S. and Germany are larger than their bilateral FDI links.

> 23The standard deviation of the return residuals is in both cases .07.

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