Before revision: Since Bartik (1991), it has become popular in empirical studies to estimate regressions in which the variable of interest is a shift-share  , such as when a regional labor market outcome is regressed on a weighted average of observed sectoral shocks, using the regional sector shares as weights.
After revision: We study inference in shift-share , such as when a regional labor market outcome is regressed on a weighted average of observed sectoral shocks, using the regional sector shares as weights.