In a paper co-authored with Sustainability Council executive director Simon Terry,"Economic Gains and Costs from the TPP", Bertram challenges some of the assumptions underpinning the modelling.
Petri et al have assumed that half of the trade gains TPP members will derive come from new entrants to exporting rather than from lowering the costs of existing exporters.
"The assumption that half of the trade costs represented by tariffs and tariff-equivalent non-tariff barriers are fixed costs ('associated with entering an export market') is simply that, an assumption, for which no reason is offered."
A more fundamental criticism of the model is that it has taken what is a standard and respectable approach to estimating the benefits of cutting tariffs on goods and extended it to cover non-tariff barriers on services.
The usual economic theory of comparative advantage and gains from trade, which rests on assumptions about perfectly competitive markets, cannot be simply extended to services many of which are characterised by imperfect competition arising from such things as intellectual property and brand-protection measures, regulations intended to ensure quality of service and government funding, Bertram argues.
"Indeed, there is no generally accepted economic theory of gains from international trade in such markets, because of the arrangements protecting intellectual property and other devices which exclude potentially more efficient competitors from markets in which incumbent suppliers have established their positions and brands."
There is no good theory that says expanding intellectual property rights internationally gives clear gains to all parties, he says.
In effect the proponents of TPP drape the mantle of free trade around a range of measures designed to entrench and protect the position of incumbent firms rather than facilitate competition and innovation.
Another area of non-tariff barriers whose elimination is modelled simply as reductions in trade costs is international finance. Here the reduction of barriers involves limiting the ability of national governments to regulate their financial sectors and requiring them to accept investor-state arbitration in an international tribunal to resolve disputes with foreign-owned banks.
"These are all entered into the ... analysis as cost reductions for the exporters of financial services, without regard to the growing worldwide realisation that effective financial regulation is essential in the wake of the global financial crisis."
About a third of the claimed benefits of TPP for New Zealand are attributed to foreign direct investment rather than trade.
Petri et al offer an estimate of what each TPP country's level of inward foreign direct investment would be in a world with no barriers, based on the size of its economy, its gross domestic product per capita (to reflect its level of development) and its ranking in the World Bank's ease of doing business table.
They then compare the actual level of inward FDI with that potential and assume - that word again - TPP is capable of moving each country two-thirds of the way towards it.
They cite no research on empirically observed links between international agreements and actual investment changes, Bertram says, and they assume that every $1 of FDI from one TPP country to another will generate 33c of increased output per year, which they count as a net gain split equally between the country making and the country receiving the investment.
"If one were talking about net increases in total capital stock resulting from increased aggregate saving, numbers of this magnitude might be relevant," he said. "But an increase in the FDI stock is not the same thing as an increase in capital stock."
Much, if not most, of the inbound FDI in New Zealand has consisted of the purchase of existing assets and businesses. Bertram concludes that the figures cited for "FDI effects" are entirely arbitrary.
The review reckons that less than a quarter of the gains projected for the TPP economies overall rest on solid analytical foundations. And those gains have to be balanced against costs which Petri et al have not counted.
Bertram and Terry quote from another review, by the New Zealand Institute of Economic Research's John Ballingall in 2012, who said, "It is difficult if not impossible to use [computable general equilibrium] models to examine some of the TPP policy issues that are attracting a lot of attention from critics of the agreement such as investor-state dispute settlement, the potential risks to Pharmac, plain packaging cigarettes, etc."
More generally TPP would impose limits on governments' ability to regulate in what they deem to be the interests of their people, including in such areas a preferential government procurement or capital controls to curb destabilising or speculative cross-border financial flows.
They conclude that the TPP offers only small quantifiable benefits from trade liberalisation bundled up with fundamental, hard-to-quantify losses from investor-state dispute resolution and other limitations on a government's ability to protect the public interest.