Dix-Carneiro and Kovak Trade Reform and Regional Dynamics industries, variation in the industry distribution of employment in each region generates substantial variation in _RTCr_ . Appendix A.3 shows similar figures for a variety of other regions throughout the country, showing how differences in industry mix drive geographic variation in _RTCr_ .

This variation is presented in Figure 3. Regions facing larger tariff cuts are presented as darker and bluer, while regions facing smaller cuts are shown as lighter and yellower. The region at the 10th percentile faced a tariff decline of 13.8 percentage points, while the region at the 90th percentile faced a 4.2 percentage point decline. Hence, in interpreting the regression estimates below, we compare regions whose values of _RTCr_ differ by 10 percentage points, closely approximating the 90-10 gap of 9.6 percentage points. Note that there is substantial variation in the tariff shocks even among local labor markets within the same state. As we include state fixed effects in our analyses, these within-state differences provide the identifying variation in our study.<sup>20</sup> Note that our theoretical framework rationalizing the use of _RTCr_ as a valid measure of tradeinduced local labor demand shocks assumes that workers are homogeneous, perfect substitutes in production, and perfectly mobile across industries within regions. These assumptions limit our ability to interpret heterogeneous effects of regional tariff changes on wages and employment of workers with different skills and initially employed in different industries. Therefore, we refrain from reporting heterogeneous effects of _RTCr_ on the various labor market outcomes studied in this paper and postpone such an investigation to future work extending our framework to accommodate heterogeneous workers and complementarities in production.<sup>21</sup> In the following two sections, we implement empirical analyses at the regional and individual levels. In both cases, we examine how post-liberalization (1995-2010) labor market outcomes evolved for regions facing larger tariff cuts vs. regions facing smaller tariff cuts. Thus, we essentially use a regional difference-in-differences approach with a continuous treatment given by _RTCr_ . This approach allows us to generate credible estimates of the causal regional effects of liberalization, but cannot capture overall national effects of liberalization that apply across regions. This feature is common to all studies utilizing cross-industry or cross-region variation for identifying the effects of liberalization.

Our approach parallels prior studies examining the local effects of trade liberalization. However, the RAIS data allow us to calculate changes in regional outcomes in each year following liberalization, so rather than observe liberalization’s local effect in one post-shock period, we trace out the dynamic regional response to liberalization as it evolves over time. We also include controls for pre-liberalization trends that might otherwise confound this research design, with little effect on the estimates. The following two sections describe our detailed estimation strategies and findings.

> 20A regression of _RTCr_ on state fixed effects yields an _R_ 2 of 0.23; i.e. 77% of the variation in _RTCr_ is not explained by state effects. Our main conclusions are unaffected by the inclusion or exclusion of state fixed effects.

> 21In this case, there will no longer be a unique local labor demand shock, but rather different local labor demand shocks facing heterogeneous workers. Because of complementarities, a local labor demand shock to skilled workers will also affect unskilled workers’ outcomes in such a way that local labor demand shocks across skill levels will all be intertwined, as shown in Dix-Carneiro and Kovak (2015).

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