Second, the predicted values of MTCs used in models 4-6 properly include the effect of variables such as distance or contiguity whose impact on the value of trade should mainly work through raising transport costs. This is exactly what we find. Compared to their coefficients in columns 1-3, the direct effect of distance and contiguity either vanishes or is substantially reduced. The significant distance coefficient in column 4 may reflect a selection effect<sup>22</sup> but distance is insignificant in columns 5 and 6. Contiguity has a direct effect only in the full sample including zero trade flows but no effect once only positive seaborne trade flows are considered, which is precisely what we would expect. In contrast, the presence of a PTA directly affects trade flows without raising transport costs, and this prediction is borne out by the fact that the PTA coefficient is significant and of roughly equal size across all 6 columns. These results demonstrate the usefulness of the two-step approach for correctly quantifying the impact on trade flows of policy measures and other gravity variables. For instance, if one simply estimated the effect of distance on trade flows, conditional on contiguity, PTAs and tariffs, but not otherwise accounting for maritime transport costs, one would obtain a distance elasticity of trade of –3.1. In contrast, the distance elasticity implied by model 4 in Table 4, which incorporates both the main effect through MTCs as well as a potential direct effect, would amount to –1.6 only.<sup>23</sup> Thus without taking proper account of MTCs, estimates of distance elasticities may be severely biased.<sup>24</sup> Of particular interest is a quantification of the effect of investment restrictions on seaborne trade as these kinds of frictions have not been studied before. Table 5 shows that the trade depressing effects, in percentage terms, of policy barriers through raising transport costs is sizable.<sup>25</sup> Across all three columns, the effect of policy restrictiveness is nonlinear but

> 22  In addition to the first-order effect of distance on marginal costs, which is rolled into predicted MTCs, distance may exert a direct effect through specialisation.  Harrigan (2010) has shown that in the presence of alternative transport modes which differ in their cost/speed trade-off, and consumers valuing timeliness of delivery, distance will play a role in determining comparative advantage.  Using US import data, Harrigan shows that faraway exporters have a relatively high market share in goods which are transported by air (as opposed to surface), implying that in a sample restricted to seaborne trade flows and controlling for contiguity, distance exerts a negative effect via comparative advantage specialization.

> 23  We compute this quantity by calculating the marginal effect on the censored mean with respect to distance in elasticity terms from the first stage (unrestricted and restricted sample) and then multiply the results with the cost elasticity of trade from the second stage as shown in columns 4 and 5, respectively.  In so doing we take care of the retransformation problem on both sides of the first-stage equation, for what is needed is the elasticity of _MTCs_ with respect to _distance_ while the estimable equation is framed in terms of _log(MTC)_ on _log(distance)_ . 24  Egger (2008) has shown in a general gravity framework (not specific to seaborne trade) that the marginal effect of distance may differ across country pairs.  Here we argue that, heterogeneous effects notwithstanding, even the average effect may be biased if distance were solely and directly used as a transport cost proxy.

> 25  For columns 1 and 2, we compute this quantity by first calculating, for each STRI quartile, the marginal effect on the censored expected value of trade costs in the first stage, and then evaluate the predictive margins for the value of imports in the second stage at each of these values for predicted MTC.  We then express the change in

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