To deal with those problems, we adopt three different strategies. First, we clear out the effect of – one source of – on our productivity growth presumed endogeneity prices by regressing transport cost series on industry multi-factor productivity indices (from the klems database), as well as industry and year fixed effects. We then use the residual from that regression as a proxy for the transportation cost series. By definition, that residual is orthogonal to any productivity-driven price changes that could stem from the changing geographic concentration of industries. This strategy does not deal directly with the transportation price index.

Second, we use us manufacturing industry price indices as external instruments for the transport cost series. This instrumentation strategy is similar to that of Ellison _et al._ (2010), who instrument the us input-output tables and the us industry labor requirements with those of the uk. The underlying idea is the following. Assume that the geographic concentration of an industry increases over time because of unobserved factors that we cannot control for in our analysis. This increasing geographic concentration then raises ad valorem transport costs via price decreases of the industry’s output. Provided that the changes for the us are not driven by the same unobserved factors that affect the spatial concentration of the industry in Canada, but that the us price series **P**<sup>US</sup> trans, _t_<sup>/</sup><sup>**P**US</sup> _i_ , _t_<sup>arecorrelatedwiththechangesin</sup><sup>**P**trans,</sup><sup>_t_/</sup><sup>**P**</sup><sup>_i_,</sup><sup>_t_,theywill</sup> provide valid instruments for the Canadian transport cost series. Two potential limitations of these instruments are the following: (i) there may be common underlying unobserved factors that drive changes in the concentration of the same industries in Canada and in the us; or (ii) the geographic concentration of an industry in Canada affects directly the productivity – and, therefore, the price indices – in the us. While we cannot completely rule out those possibilities, neither strikes us as very plausible. First, the panel nature of our data and the extensive set of time-varying controls should pick up most of the unobserved factors that may drive the increasing concentration of the industry; and second, the Canadian economy is small to the us so that in the concentration in Canada are compared economy, changes geographic very unlikely to have substantial productivity impacts in the us.<sup>14</sup> Last, as we have a large number of industries and a fairly long time series, our setting lends itself reasonably well to the construction of internal instruments. We implement the method suggested by Lewbel (2012), which exploits heteroscedasticity and variance-covariance restrictions to obtain identification with 2sls when some variables are endogenous and when external instruments are either weak or not available. C more details on Appendix provides this method. We use this approach to deal with remaining potential endogeneity issues in our trade exposure and input-output distance measures (see Appendices B.2 and B.3 for a

> 14The elasticity of productivity to the density or size of economic activity is usually in the 3–8 percent range. Hence, huge changes in the geographic structure are needed to obtain large productivity changes. Furthermore, given that the Canadian economy is ten times smaller than the us economy, shocks to Canadian productivity have very limited effects on the us, safe for a couple of states relatively close to the border or a couple of borderspanning industry networks (like the automotive industry). Excluding the automotive industries (naics 3361, 3362, and 3363) has no qualitative effect on the ‘ad valorem trucking cost (residual)’ coefficient.

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