described in this section is all about our suspicion that there is some trade and output data even though it is not observed. In this case, rather than dropping the exporter-year fixed effect of _i_ in sector _k_ and setting _Y_<sup>ˆ</sup> _i_<sup>_k_= 0,weexploitthepanelstructureandtheproperties</sup> of the PPML estimator to generate consistent estimates of output.

Taking the very strong stand that structural gravity generates the true data, these generated activity variables _{Y_<sup>�</sup> _i_<sup>_k,E_�</sup> _j_<sup>_k}_areperfectlyconsistentwiththetheory.Theirexpected</sup> value (asymptotically) is the true value. In reality, both the fitted values _Y_<sup>�</sup> _i_<sup>_k_andtheob-</sup> served values ( _Yi_<sup>_k_)</sup><sup>_∗_aremeasuredwitherror,andthemeasurementerroroftheobserved</sup> values might contaminate the estimates of the _τij_<sup>_k_’ssuchthatthefittedvaluesof(14)and</sup> (15) are not asymptotically unbiased.<sup>22</sup> The primary challenge to implementing the system of equations (14)-(15) lies in the fact that, by definition, one crucial component ( _β_<sup>ˆ</sup> _it,_<sup>_k_</sup> 6<sup>)ofthetradecostfunction</sup><sup>_τ k_</sup> _ij_<sup>cannot</sup> be estimated when output is missing or suspect. To see this, recall that the indicator for internal trade is the only variable that carries direct information on output. Thus we now turn to the issue of estimating border effects in the next section, in which we capitalize on the newly-created multi-dimensional database of border estimates from Section 4.3 to study their determinants.

# **5.2 On the Determinants of Border in Services Trade**

The wide variability across border estimates in each dimension (across countries, sectors, and time) sets the stage for meaningful econometric analysis. The contributions of this section are twofold. First, the empirical results from ‘border estimations’ add to our understanding

> 22Considering the potentially most problematic contamination issue is somewhat reassuring. The internal trade flows are typically generated as a residual ( _Xii_<sup>_k_)</sup><sup>_∗_=(</sup><sup>_Y_</sup> _i_<sup>_k_)</sup><sup>_∗−_�</sup> _j_ = _i_<sup>(</sup><sup>_X_</sup> _ij_<sup>_k_)</sup><sup>_∗_.Theeconometricmodel</sup> assumes that the observed bilateral trade flow value is related to the true value by ( _Xij_<sup>_k_)</sup><sup>_∗_=</sup><sup>_X_</sup> _ij_<sup>_kεk_</sup> _ij_<sup>where</sup><sup>_εk_</sup> _ij_ is a random error term. The gravity estimation would apply this assumption to all trade flows, internal and international. When would this assumption be met? Generating ( _Xii_<sup>_k_)</sup><sup>_∗_= (</sup><sup>_Y_</sup> _i_<sup>_k_)</sup><sup>_∗−_�</sup> _j_ = _i_<sup>(</sup><sup>_X_</sup> _ij_<sup>_k_)</sup><sup>_∗_isconsistent</sup> with ( _Xii_<sup>_k_)</sup><sup>_∗_=</sup><sup>_X_</sup> _ii_<sup>_kεk_</sup> _ii_<sup>ifandonlyif(</sup><sup>_Y_</sup> _i_<sup>_k_)</sup><sup>_∗_= �</sup> _j_<sup>_X_</sup> _ij_<sup>_kεk_</sup> _ij_<sup>;thatis,thereisnoadditionalsourceofmeasurement</sup> error in the output variables. This is a plausible assumption because statistical practice would normally include such consistency checks. But it is not guaranteed.

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