For many the US dollar will be much more significant than its 30 per cent weighting in the TWI.
For others the Australian dollar is far more important than its 22 per cent index weighting.
And remarkably, the TWI, whose composition was last revised in 1999, does not include the renminbi even though China is now New Zealand's second-largest export market and largest source of imports.
It does include the pound sterling even though the United Kingdom is now only slightly ahead of Korea in terms its two-way trade with New Zealand
Helpfully, though, the ASB Bank economists have compiled two alternative exchange rate indices, weighted by manufacturing import and export flows.
They define manufacturing narrowly, excluding the output of dairy factories and meat works, so as to reflect the position of more value-added, or in the jargon of statisticians "elaborately transformed", manufactured goods. Such goods represent about 19 per cent of exports and 51 per cent of imports.
Like the official index, it includes five currencies, but with the renminbi replacing sterling.
During the last cycle - from the recession at the start of the millennium to the more recent one - the three indices tracked each other quiet closely.
But since 2009 they have diverged.
All three have appreciated, but the index reflecting manufactured imports less so than the official TWI, and the index for manufactured exports less still.
The result is that the ASB exchange rate indices for both manufactured exports and imports, and especially the former, are even now at levels lower than they were during the boom years of the mid-2000s.
That does not mean there isn't a problem, of course.
There was plenty of collateral damage to the tradeables sector during the mid-2000s' housing and consumption-driven boom. (All the more reason to be wary of stoking another one.)
And these indices are, by their nature, averages. As the saying goes, the trouble with averages is that when Bill Gates walks into a bar the average net worth of the people in the bar shoots up, but the other patrons don't suddenly become billionaires.
But it does help to calibrate the scale of the current problem.
ASB chief economist Nick Tuffley says the fact that the manufacturing-relevant exchange rates have not climbed as much as the official TWI highlights a key difference between the most recent appreciation compared with that of the early to mid-2000s.
"In the 2000s the New Zealand dollar appreciated more broadly, that is, against most major currencies and to a similar degree against each. Since 2009, though, it has held broadly stable at a low level against the Australian dollar."
Australia is the destination for nearly half of New Zealand's manufactured exports.
"The appreciation against the Chinese renminbi has also been more muted compared to the previous decade as that currency has been strengthening against the [weak] US dollar," Tuffley said.
"Overall, the alternative exchange rate baskets we have constructed suggest that for the manufacturing sector it is import-competing businesses that appear to be facing the broader impact of the high New Zealand dollar. The competitive challenges for the manufacturing export sector are likely to be slightly lower overall and apply to exports that don't benefit from exposure to Australia."
Tuffley is quick to add, though, that firms exporting to markets such as the US, Britain and Europe face the twin challenges of unfavourable exchange rates and weak demand, and those challenges are considerable.
The Australian dollar has a weight of 44 per cent in ASB's manufacturing export weighted index.
So it is a bit of a worry that the transtasman cross rate has risen to 81c lately compared with an average 79c over the past three months.
But at these levels it is still low by the standards of the past 20 years.
By contrast the US dollar, against which the kiwi is at historically high levels, accounts for just 17 per cent of that index.
It could be argued that understates the importance of the US dollar, as a higher exchange rate against the greenback reduces the competitiveness of New Zealand goods not only in the US market, but in other markets where they have to compete with goods from the US or priced in US dollars.
It is to reflect those indirect effects that the official TWI also takes into account the size of the five trading partners' economies (although, again, with the conspicuous omission of China).
A further complication arises from the prevalence of long international supply chains in modern trade.
The trade accounts may record an imported smartphone, say, as made in China but much of the value embedded in it will have been added in other countries upstream of the final assembly.
The OECD and the World Trade Organisation have set up a database to take account of these effects.
On that value-added basis, the United States is New Zealand's largest source of imports, ahead of Australia and China, both of which outrank it in the unadjusted trade accounts.
It also means New Zealand's trade deficit with China is more than a third, or US$300 million ($355 million), smaller than the unadjusted numbers indicate.
The OECD says that on average there is a smaller foreign value-added content in New Zealand's gross exports than in other developed countries (19 per cent compared with 28 per cent across the OECD), reflecting geographical remoteness.
Among manufactured exports the foreign value added content ranges from 20 to 40 per cent.
Conversely, a relatively high proportion of the intermediate inputs New Zealand imports - such as materials and components - end up in exports.
And, echoing a point made by some of the submitters to the parliamentary inquiry into manufacturing, the OECD says that "exports of manufacturing goods incorporate a large share of value added from the services sector, highlighting the importance of services in export competitiveness and the fact that services are more traded than usually thought when taking into [account] global value chains".
It is an important point and a reminder that it is real, not nominal, exchange rates that matter for international competitiveness, and there are many influences on them.
Clearly, it is a more nuanced story than the usual one:
"Look how high the dollar is. Manufacturers have got no show."
