How serious is the omission of bilateral tariff rates in gravity?

In this paper, using the worldwide dataset of bilateral tariff rates, we explore how serious the omission of bilateral tariff rates in gravity is. Our findings are as follow. Firstly, the omission of bilateral tariff rates seems not to be so serious in terms of omitted-variable biases because the coefficients for the usual gravity variables do not change before or after their inclusion. Secondly, while the widely-used dummy variable of regional trade agreement could not play an alternative role in place of tariff rates, the inclusion of time-invariant pair fixed effects in addition to the time-variant importer fixed effects and exporter fixed effects accounts for the omission of tariff rates. The inclusion of those fixed effects makes the coefficient for bilateral tariff rates insignificant.