agreement, is non-trivial and yet is not captured in most models because those models are not stochastic. As Francois and Martin (2004) show, even bindings that are set well above average rates of protection may greatly diminish the costs of protection when international prices peak. They estimate, for example, that the European tariff binding on wheat, at 82 percent, reduced the cost of protection to this commodity by almost a third, despite being substantially above the average rate of protection prevailing during the preceding 15 years for which data were available. This suggests our current CGE models are understating the gains from tariff and subsidy bindings, particularly for farm products.

# **_Aggregation of protection_**

Trade barriers vary enormously across commodities, and frequently also across suppliers thanks to regional and other preferential trade agreements. This variation in rates of protection increases the cost of any given ‘average’ level of protection, since the cost of protection increases with the square of the rate of protection. Necessarily, some degree of aggregation is unavoidable in modelling the real world because the available information on the structure of production and consumption is at a higher level of aggregation than information on tariffs and trade. Further aggregation is employed for computational reasons in a world of more than 225 countries, thousands of product tariff lines, many different occupations and skill levels in labor markets, etc. And additional problems are introduced by the typical approach to aggregation of trade barriers, namely, using averages weighted by external trade: as protection rates rise, the weights associated with these measures decline, which means that a tariff that completely blocks trade has the same measured impact as a zero tariff.

The modern approach to tariff aggregation provides a possible means of dealing with the aggregation problem. Anderson and Neary (1992) have developed a single tariff aggregator that captures the welfare impacts of a non-uniform tariff. Building on this approach, Bach and Martin (2001) use a tariff aggregator to capture the impacts of changes in the tariff regime on the expenditure required to achieve a given level of utility, and another to capture the impact on tariff revenues. Manole and Martin (2005) provide closed-form measures of these aggregators for the widely-used constant-elasticity-of-substitution functional form. Applying these procedures to a sample of seven developing countries, they find that appropriate aggregation increases the estimated cost of protection on average twenty-fold relative to the cost estimated using a weighted average tariff.

The problems of aggregation are particularly intense in agriculture because of the enormous variation in rates of protection across countries and commodities, especially among the industrial countries. Simple solutions, such as the representative-weighting approach used in some versions of the MAcMAP database (Bouet et al. 2004), deal with the weighting problem without addressing the aggregation bias problem associated with nonlinearity in the costs of individual tariffs. In a recent paper, James Anderson (2006) proposes a new aggregation method that deals with both the aggregation bias and weighting problems while maintaining global payment balances, allowing it to be applied in future global CGE models.

# **_Product quality and variety differences_**

A separate aggregation issue has to do with the fact that, within any product classification, there is a wide range of qualities and varieties available. The only way 35