It was the year that Deng Xiaoping set China on its reform and opening-up course when, according to Roach, its economy was "on the brink of collapse".
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"Out of necessity, both countries came together and formed a marriage of convenience. The United States needed cheap Chinese goods to make it happen. China needed foreign consumption in order to become the ultimate production machine.
"Chinese savings then became a support for America's growth model which needed Chinese demand for its treasuries (US Treasury bills)."
Roach says the problem with this codependency was that it was pushed "too hard for far too long" until cracks began to appear.
"Both economies started to feel the weight of imbalances and frictions that raised sustainability issues of their own."
He argues in the book that 2007 was the next pivotal year in the relationship.
It was Wen Jiabao, then Chinese premier, who warned the Chinese economy was "unstable, unbalanced, uncoordinated and ultimately unstable" in what has since been referred to as "The Four Uns".
"He was bold enough to make the criticism while the economy was strong and in surplus. It was also a pivotal year in the United States since in the second half we had the first manifestations of the subprime crisis that nearly brought the entire financial system to failure."
Roach says that 2013 was the third significant date in the relationship when it became clear that China had fully taken on board the dangers of co-dependency while the United States was still largely in denial.
He contrasts the whole series of economic rebalancing measures set out in the Party's Third Plenum last October against the political paralysis in the United States in its failure to agree a new federal budget.
"A month after the Third Plenum, we shut our government down for 16 days. So of the two co-dependent partners, only one accepts the need for change."
This situation where only one partner to the relationship accepts the need to change is part of the "unbalanced" nature of the two countries' relations that provides the title of Roach's book.
The author argues in the book that the relationships between the key individuals on both sides, particularly between former Federal Reserve Bank chairman Alan Greenspan and China's reforming premier Zhu Rongji and, more recently, Wen and Greenspan's successor, Ben Bernanke, have been intriguing. His book devotes a couple of chapters to this.
"Despite coming from different systems, the problems they had to grapple with were in many ways similar. They were also people who knew each other and therefore had an understanding of each other's issues."
One issue that has provided a distraction for policymakers has been the financial crisis.
Does Roach believe that the global economy is beginning to move away at last from the disaster that befell it six years ago?
"I think the problem is that we are moving so slowly that it still looms larger in the rearview mirror than we would like.
"The US is widely viewed as the engine of the developed world, but it is not much of an engine if it can produce only zero growth, as it did in the first half of this year."
Roach is interested in the debate prompted by French economist Thomas Piketty's book, Capital in the Twenty-First Century, which he is one of the few to have read cover to cover, if the recent Amazon survey is to be believed.
"I like the book. It is perhaps too long and covers too much, but there is a lot of valuable data and good insights that give you pause. I think he (Piketty) perhaps views himself more as a challenge to the economic orthodoxy than he actually is."
As for China, which Roach has visited four times already this year, he is confident about the current economic reforms.
"Last year was the first time in modern Chinese history when the tertiary or services sector was larger than the secondary one," he says.