Which they did by comparing exports before and after the abolition of the barriers, and found what good economists would expect;
...we find that the post-quota export growth and price declines of quota-bound versus quota-free goods [from the previous quotas] are dominated by [new] entrants rather than incumbents. Furthermore, we show that the entrants behind this trend are primarily privately owned domestic and foreign firms, and that their growth comes at the expense of state-owned enterprises, who are on average nearly a third less productive than their private-sector counterparts. Additional evidence of misallocation comes from the fact that nearly two-thirds of the price decline observed in the year quotas are removed is due to entrants rather than incumbents. These trends provide strong evidence against the hypothesis that quota licences were allocated on the basis of firm efficiency.I.e it eliminated the advantages of bribery. So there are gains to be had even in excess of what some trade models predict.