Section 4.1 claims that the coefficient on our firm variable will always be at the upper bound, as we are using establishments rather than firms. This seems to be intuitively wrong, given that we are estimating the model in log differences, so that level effects are removed from the estimation.
Maybe this should lead us to think more closely about the "firm" measure in model terms. My understanding is that the Melitz/Ottaviano model has unit labor input, so number of firms = number of establishments = number of workers. However, some of the papers we ourselves are citing show empirically that trade liberalization favors larger firms, who reap the productivity gains. This implies that different patterns in the pass-through from employment to establishments to firms yield different productivity results (e.g. an increase in the number of establishments relative to the number of firms would mean firms are getting bigger, and hence more productive, but this wouldn't show in the number of firms, which would stay constant).
Section 4.1 claims that the coefficient on our firm variable will always be at the upper bound, as we are using establishments rather than firms. This seems to be intuitively wrong, given that we are estimating the model in log differences, so that level effects are removed from the estimation.
Maybe this should lead us to think more closely about the "firm" measure in model terms. My understanding is that the Melitz/Ottaviano model has unit labor input, so number of firms = number of establishments = number of workers. However, some of the papers we ourselves are citing show empirically that trade liberalization favors larger firms, who reap the productivity gains. This implies that different patterns in the pass-through from employment to establishments to firms yield different productivity results (e.g. an increase in the number of establishments relative to the number of firms would mean firms are getting bigger, and hence more productive, but this wouldn't show in the number of firms, which would stay constant).