Perhaps more accurately, we should say one of the problems with the work of Thomas Piketty. As Brad Delong points out, the central contention is as follows: Hotshot French economist Thomas Piketty, of the Paris School of Economics, looked at the major democracies with North Atlantic coastlines over the past couple of centuries. He saw five striking facts:
First, ownership of private wealth—with its power to command resources, dictate where and how people would work, and shape politics—was always highly concentrated. Second, 150 years—six generations—ago, the ratio of a country’s total private wealth to its total annual income was about six. Third, 50 years—two generations—ago, that capital-income ratio was about three. Fourth, over the past two generations that capital-income ratio has been rising rapidly.
At first sight this is indeed a problem. The capital of our economy is what we produce our income from. If the capital to income ratio falls then that means we are using the capital more efficiently. If it rises, obviously and equally so, the economy as a whole is becoming less efficient at turning assets into income. However, we need to break this out into more than just "capital".
Using the work of Saez and Zucman we can see that at least on this side of the Atlantic the great capital concentration of the late 19th century was in the value of agricultural land. As the Americas, then the Ukraine, opened up this value fell precipitately. Thus the destruction of the great aristocratic landed fortunes.
The privately held value of financial instruments hasn't really changed all that much over the time period: and that's the bit we usually concern ourselves with when we talk about wealth concentration.
In more recent decades the two components of wealth that have risen again are private land holdings, and that is principally domestic housing and private pensions savings. Again, that privately held value of financial assets, outside those pensions, hasn't really risen nor has it become more concentrated.
So, yes, we've had a rise in the capital to GDP ratio. That part that is house price rises, well, we've had our say about that a number of times. It's the restriction on planning permissions which has driven up the value of land you may build upon. This is inefficient and we have suggested, again a number of times, that we should do something about it. Like destroy the system which artificially restricts, and thus drives up, the price of those permissions.
As to the private pensions this is actually something of a success story. Immediately post WWII someone retiring at 65 could and did expect perhaps 3 to 5 years in retirement before death. Nowadays the equivalent number is 15-20 and it's still rising. Fortunately we did also have a system of pension savings provision which has largely paid for this. That's an inefficiency in the capital to income ratio we can live with: because if we didn't have it then there would be many old people with no income to live upon.
Given that Piketty's observed facts are so easy to explain we don't really need to take much notice of his further worries. None of the above justifies a wealth tax, worries over the creation of a permanent haute bourgeoisie or any of those other fashionable concerns. Fix the planning system and celebrate pensions and we're done.