It is common to recognize that tariffs have gradually been replaced by nontariff barriers (NTBs). Some authors go even further and argue there is a "Law of Constant Protection" (an expression used by Bhagwati  mainly to dismiss the idea). Baldwin (1984, 600), for instance, writes: "Not only have these measures become more visible as tariffs have declined significantly through successive multilateral trade negotiations but they have been used more extensively by governments to attain the protectionist goals formerly achieved with tariffs."
The purpose of this article is to set up a model in which the effect of trade liberalization on the use of quotas and antidumping laws can be investigated directly. We analyze two types of bilateral trade liberalization: tariff reductions and quota elimination. We show that our model is consistent with a progression from the use of tariffs only to the use of quotas (following tariff liberalization) to the use of antidumping laws (when quotas have been jointly tarrified). Second, it is also consistent with a narrowing of the range of industries in which each of these instruments is used. Third, the extent of bilateral tariff liberalization and the ensuing degree of replacement of tariffs by NTBs depend on the combination of two industry-specific characteristics: the government's preferences for domestic firm profits and the importance of international transport cost in the industry. Overall, our results suggest that treaties that remove or reduce one type of distortion may lead to the use of other policies tha t are even worse, but despite the use of NTBs overall trade is more liberal.
To show these results, we use a standard two-country model with two-way trade where the policy maker's objective function is quasi-concave. This last characteristic is important to explain some of the results as it leads to strategic complementarity in the tariff game and to the possibility of interior solutions in the quota game.
Our results appear to track three separate sets of empirical facts well. First, evidence shows that there is a clear emergence of quantitative restrictions in the 1960s in manufacturing sectors and in developed economies followed by an explosion in the use of antidumping constraints since the 1980s. (1) The emergence of these two NTBs can be linked to preceding multilateral trade rounds and in particular to the completion of the Kennedy Round. Today, the General Agreement on Tariffs and Trade (GATT, 1990, 10) notes that "despite a recent decline in the number of anti-dumping investigations initiated in the United States and the European Communities, anti-dumping remains (after tariffs) the most frequently invoked trade policies in these countries." Antidumping measures are also spreading to developing countries (Nogues, 1993). Quantitative restrictions are meanwhile on the decline as signatories of the Uruguay Round agreement are now required to "tariffy" existing quotas and constrain their future use. GATT ( 1990) documents specific import quotas, import licensing restrictions, and items subject to import prohibition that have been eliminated in recent years.
Second, the gradual replacement of trade tools has also been accompanied by a reduction of the number of sectors affected by NTBs. Whereas very few products were traded without levy before the various GAIT rounds, Renner (1971) finds that 7% of the (four-digit) product classes were affected by quantitative restrictions in the United States and in the European Communities in 1970. The number of antidumping cases in the European Communities (initiated and/or ending up with a positive decision) represents a fraction of this number (see GAIT, 1993b) mainly concentrated on a very small number of sectors (see Messerlin and Reed, 1995). Of course, it is not because a smaller number of sectors are affected by NTBs that overall protection necessarily decreases. However, given the high rates of growth in world trade, it seems likely that despite this substitution the overall level of protection has decreased over time. …