THE Trans-Pacific Partnership (TPP), a putative trade agreement, would ease commerce between America, Japan and ten other countries that between them account for two-fifths of global GDP. But how beneficial would it be to these economies? Advocates claim it would boost their output by nearly $300 billion in a decade. Critics say it would make little or no difference.

The disagreement reflects the difficulty of gauging the impact of free-trade agreements. Almost all economists accept the benefits of free trade as laid out in the early 1800s by David Ricardo. Countries do well when they focus on what they are relatively good at producing. But Ricardo looked at only two countries making two products, at a time when few non-tariff barriers such as safety standards existed. This renders his elegant model about as useful for analysing contemporary free-trade deals as a horse and carriage are for predicting the trajectory of an aircraft.

Instead, most economists use what is known as computable general equilibrium (CGE) analysis. CGE models are built on top of a database that seeks to describe economies in full, factoring in incomes, profits and more. Researchers line things up so that the model yields the same output as a real benchmark year. Once that is achieved, they “shock” the model, adjusting trade barriers to see how outcomes shift, both immediately and over time.

There is much to recommend CGE. It is the only trade model broad enough to encompass services, investment and regulations, all of which lie at heart of the TPP debate. It also generates predictions that policymakers want: which sectors will do well and how incomes will change. But CGE has big drawbacks. First, it is dependent on data, which can be very patchy in some areas. Second, faulty assumptions can quickly lead forecasts astray.

Studies of TPP illustrate these strengths and weaknesses. The most influential, by Peter Petri, Michael Plummer and Fan Zhai, for the East-West Centre, a research institute, forecasts that the deal would raise the GDP of the 12 signatories by $285 billion, or 0.9%, by 2025. It is their numbers that America’s government cites when it says TPP will make the country $77 billion richer. Their model tries to avoid some of the common failings of CGE. Their assumptions are transparent, include a range of scenarios and are often conservative—for example, they expect only slow and partial implementation. That makes the results more credible.

Yet subjective elements of the model have a huge impact. The authors use a new approach to predict that more firms will become exporters as the costs of trade decrease. That may be an improvement over previous theories, which assumed a constant number of exporters, but this one tweak greatly changes results: it makes the benefits some 70% bigger, according to a study for Canada’s C.D. Howe Institute by Dan Ciuriak and Jingliang Xiao.

Some assumptions are also debatable. The researchers calculate that increased protection of intellectual property (IP) is beneficial for all countries. A review of studies of TPP funded by the British government, by Badri Narayanan, Mr Ciuriak and Harsha Vardhana Singh, questions that. Stronger protection for IP should spur more investment by producers. But it can also raise costs for consumers beyond what is necessary to encourage innovation and slow the spread of technology to developing nations.

That also points to one of the many blind spots in CGE models. Most use figures from Purdue University’s Global Trade Analysis Project, the best database available. But since it was initially developed for agriculture, it is skewed. It has separate categories for raw milk and dairy products, but lumps pharmaceuticals into one overarching category for chemicals—a problem for models since TPP deals extensively with drugmakers’ IP. Given the uncertainty, Messrs Ciuriak and Xiao exclude any impact from enhanced protection of IP. They also use a more conventional model for exports. They calculate that TPP will raise the GDP of the 12 countries by just $74 billion by 2035, a mere 0.21% higher than baseline forecasts. Others see an even smaller impact. In a paper for the Asian Development Bank Institute, Inkyo Cheong forecasts that America’s GDP will be entirely unchanged by TPP.

Why bother?

That raises the question of whether TPP is worth pursuing at all. As complex as the CGE studies are, they are just models, peering into the future through a haze of assumptions. It is thus important to buttress them with studies of completed deals. The Asia-Pacific region is an ideal laboratory because it went from five free-trade agreements in 1990 to more than 200 in 2015. A new Asia-Pacific Economic Cooperation study finds that, in the five years after an agreement, participants’ exports increased on average by nearly 50% relative to the five prior years. The researchers then control for factors such as GDP and distance, isolating free-trade deals as a variable. Those with the biggest impact share certain features: they have more members, bring together developed and developing economies, and aim at non-tariff barriers as well as tariffs.

This suggests that the gains to be had from freeing trade, even if diminishing, are far from exhausted. But that does not necessarily make TPP the right way forward. Almost all studies agree that its principal limitation is size: it is not big enough. Specifically, the exclusion of China is costly. The Petri study concludes that a more inclusive Pacific free-trade deal with weaker rules on state-owned firms and intellectual property would lift income gains for the original 12 TPP members, including America, to $760 billion—more than double the boost from TPP. Such precise CGE forecasts ought to be taken with a pinch of salt. But the moral is clear enough. The objective should be to bring more countries into the tent, not to push for overly strict rules.