also changed. To identify the causal effect of changes in the latter on changes in the former, we now turn to multivariate analysis. We work at the industry-year level and take advantage of the panel nature of our data. More precisely, we estimate the following model: where _γi_ , _t_ ( _d_ ) is the _K_ -density cdf for industry _i_ in year _t_ at distance _d_ ; _Ti_ , _t_ is our measure of ad valorem transport costs (4) of industry _i_ in year _t_ ; **X** _i_ , _t_ is a vector of time-varying industry controls measures of international trade and links between (including exposure input-output industries; see Appendices B.2 and B.3 for details on how we construct those measures); _αt_ and _μi_ are year and industry fixed effects, respectively; and _εi_ , _t_ is the error term.<sup>10</sup> The latter is assumed to be independently and identically distributed with the usual properties for consistency of ols. Our main coefficient of interest is _βT_ , which captures the impact of changes in transport costs on changes in the geographic concentration of industries.

# **.2 4 Identification issues**

In order for _βT_ to capture the causal effect of changes in transport costs on geographic concentration, we need to address a number of identification issues. In general, the two main that the of the determinants of concentration are problems plague identification geographic omitted variables and reverse causality (see Combes and Gobillon, 2015, for a recent survey). All studies based on cross-sectional industry data (e.g., Rosenthal and Strange, 2001; Ellison _et al._ , 2010) are potentially prone to these identification problems and use different strategies to overcome them. We first discuss the omitted variables problem and explain the large number of controls that we include in our panel estimations of (5) to deal with it. We then turn to the reverse causality problem and detail our instrumentation strategies. Table 8 in Appendix B.1 summarizes our main variables and provides descriptive statistics.

> 10One may be worried that identification in (5) comes from the _within_ variation in the data. The latter could be small given yearly data, especially for the spatial variables. This point has been made in other studies (e.g., Ellison _et al._ , 2010, p.1200), but those studies usually use more aggregated measures of agglomeration. Those measures change much more slowly over time than the _K_ -densities, especially at short distances. The reason is that our microgeographic measures are constructed from geocoded data, and that there is a lot of churning (entry and exit) at short distances. This is not picked up by spatially more aggregated measures, but it is by ours. Substantial plant-level churning creates a tension. One the one hand, there is _a lot of year-on-year variation_ , which allows for identification using within variation (see Table 3). On the other hand, there is also _a lot of noise_ at a small geographical scale, which makes the estimates less precise. The _K_ -density cdfs are kernel-smoothed across distances, which reduces the noise due to plant-level churning (see our cepr discussion paper version for additional details). Smoothing is also a standard procedure when working with the asm longitudinal files (e.g., Statistics Canada usually uses three-year moving averages to filter noise in these series).

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