To understand Piketty's reply, it's useful to start with the structure of Giles' critique:
- Piketty made numerous small errors or unexplained choices in constructing the wealth inequality data series for France, Sweden, the US, and the UK.
- Piketty chose to present an unweighted average of Sweden, France, and the UK as a series for "Europe."
- Piketty vastly overstated the recent rise in wealth inequality in the UK.
- By combining 2 and 3, Piketty created a Europe-wise increase in wealth inequality that is not present in the data.
- Combining 4 with 1 we can see that Piketty is a shady character.
Piketty responds by noting that despite the sweeping nature of Giles' condemnation of him, their actual disagreement is very narrow. It concerns whether or not we should compare historical data on UK wealth inequality available from tax records to more recent survey data reported by the Office of National Statistics. According to Piketty, the reason to avoid survey data is it is unreliable:
What is troubling about the FT methodological choices is that they use the estimates based upon estate tax statistics for the older decades (until the 1980s), and then they shift to the survey based estimates for the more recent period. This is problematic because we know that in every country wealth surveys tend to underestimate top wealth shares as compared to estimates based upon administrative fiscal data. Therefore such a methodological choice is bound to bias the results in the direction of declining inequality.
For instance, as I note in the technical appendix to chapter 10 (available here), the recent wealth surveys undertaken by INSEE in 2004-2010 in France indicate a top decile share just above 50% of the total wealth, whereas fiscal data (inheritance and wealth tax) suggest a top decile share above 60% of the total wealth. The gap seems particularly large for the case of Britain, which could reflect the fact that the "wealth and assets survey" seems particularly bad at measuring the top part of the wealth distribution of the UK. Indeed, according to the latest report by the Office of national statistics (ONS), the response rate for this survey was only 64% in 2010-2012; this is an improvement as compared to the response rate of 55% that was observed during the 2006-2008 wave of the same survey (see ONS 2014, Table 7.1); but it is pretty clear that with such a low response rate, it is hard to claim that one can adequately measure wealth inequality, particularly at the top of the distribution.
Also note that a 44% wealth share for the top 10% (and a 12.5% wealth share for the top 1%, according to the FT) would mean that Britain is currently one the most egalitarian countries in history in terms of wealth distribution; in particular this would mean that Britain is a lot more equal that Sweden, and in fact a lot more equal than what Sweden as ever been(including in the 1980s). This does not look particularly plausible.
Backing out, Piketty then agrees with Giles that the simple averaging of the UK, Sweden, and France is not ideal. But since calculating the UK number his way the patterns look the same no matter how you average it, this doesn't matter.
So we're left with Giles nitpicking some of Piketty's choices about France, the US, and Sweden. If you care to read the document, Piketty has replies to those nitpicks. But Piketty and Giles' bottom lines about those countries aren't actually very different so you, as a reader, are free to not care.