Do Non-Productive Investments Need to Be Written Down in GDP Accounting?

I think you are misunderstanding the discussion there.

There is no ambiguity or disagreement on what steps are taken to calculate GDP or what items are included/excluded etc. National/international agencies have handbooks with set rules, for example, US Bureau of Economic Analysis has its NIPA handbook. So you can always just go there an check the methodology. Under most standard methodologies there is no adjustment or even difference made between productive or non-productive investment. However, there are disagreements on whether GDP actually appropriately captures economic activity and if it is comparable between countries.

Pettis in that article does not say that China literally miscalculates GDP by not excluding non-productive investment. Rather disagreement here is what the GDP actually measures.

GDP’s intended purpose is to measure the value of output produced by a nation. but it is imperfect measure. For example, economists generally agree that house production is important part of economic activity, but it is hard to measure so it is excluded in GDP (this holds for many other economic activities such as those taking place in grey or black markets). In fact in his report to U.S. Congress Kuznets (who is the person who developed the modern concept of GDP) mentions in a preface that national product (GDP) in his view should encompass all production at its hypothetical market value. But he later concludes that it is difficult to properly measure non-market activity so it is excluded from the calculation. This is not an issue as long as all countries have approximately the same level of these hard to measure activities but it would create a problem in international comparisons if different countries have different levels of home production and other non included activities.

For example, in some agrarian society almost all if not all production might be done at home. So statisticians trying to record GDP for such society using the standard methodology could report 0 GDP (in hypothetical case all production is done at home & gray markets), but that obviously does not mean that there is no economic activity going on or that country has no valuable output. This is just a limitation of the GDP, GDP is not economic activity, it is proxy for it (for example, in world without thermometer you might measure temperature just by touching things and feeling if they are more hot or cold, but that would obviously create problems in interpersonal comparisons).

In cases where you know that countries in your sample have widely different levels of home production, if you want to do some more nuanced international comparison of GDP, you would do some extra research to try to find out what the value of home production is (nowadays there are some ways how this can be more or less precisely estimated) and you could try to adjust countries GDP for this problem.

Similarly, in that article Pettis does not say that GDP is miscalculated, in a sense that Chinese statisticians did not follow standard procedures. Rather there Pettis argues that because (in his opinion) a lot of Chinese investment is unproductive, compared to other countries, and according to Pettis this means that total factor productivity (TFP) for China (which is calculated using GDP), cannot be easily compared to TFP in other countries.

So, it is not that Pettis says GDP is literally miscalculated, rather he states that GDP and TFP in China cannot be readily compared to other countries. Then he goes on to propose some ways how GDP could be adjusted to compensate for that. Such adjustments are often controversial because there is large number of different ways of how one can adjust GDP and there is no clear agreement on which one is the best. In fact, going back to the previous example, the reason why GDP still excludes home production even though virtually all economists would agree its important part of the economy is that there we too do not have any agreed upon way to measure home production (at least not to such an objective degree as we can market production). So such proposals are often criticized because people do not agree on how the correct adjustment should be and thus many people even in research prefer to just default to using GDP as recorded as it is at least objective.