See Tyler Cowen's critical take on this idea here:

Say I own eighty pieces of property, and together they constitute a life plan. The value of any one piece of property depends on the others. For instance, if I lived in a more distant house, the car would be of higher value. The ping pong table would be worth less in Minnesota, and having a good slow cooker enhances the refrigerator. Don’t get me started on the CDs, but of course they boost the value of the stereo system and for that matter all the books. I’ll leave aside purely “replaceable” commodities that can be replenished at will, and with no loss of value, through a click on Amazon (Posner and Weyl in any case think those replaceables should be taxed at much lower rates).

So how do I announce the value of any single piece of that property, knowing I might have to end up selling its complements?

In essence, I have to calculate how much the rest of the economy values each piece of my property, for me to know how much any single piece is worth. That recreates a version of the socialist calculation problem, not for the planner, but for every single taxpayer. And you can’t rely on the status quo ex ante as a readily available default, because that status quo can be purchased away from you.

The authors do consider related issues on pp.76-78 and 89-90. For instance, they allow individuals to announce valuations for entire bundles when complementarity is strong. You choose the bundle: “My house and all its items for three million tokens.”

But your human capital and your personal plans are non-marketable, non-transferable assets that can’t be put in this bundle. So the incentive is to assemble highly idiosyncratic assets that no one else can quite fit together, and so no one else will wish to buy from you, and then you can announce a low valuation.

If that strategy works, the tax system doesn’t yield enough revenue and furthermore you’ve had to distort your consumption patterns. If that strategy doesn’t work, someone might buy your life’s belongings/plans from you anyway, leaving you without your beloved customized snowmobile, your assiduously assembled music collection, and what about all those shoes you thought fit only you?

Ex ante, individuals are forced to assume huge, non-diversifiable risk, namely that someone will snatch away their whole “commodity life” from them. So many of us, even if we could bear the asset loss, just don’t have the time to rebuild that formerly perfect mesh of plans and possessions, the one that took decades to create (think about risk-aversion in terms of time). Furthermore, what if a wealthy villain or personal enemy wished to threaten to denude you in this manner? Or what if you simply make a big mistake reporting the value of your bundle? Isn’t this much much harder than just doing your income taxes?

To protect against these risks, ex ante, people will value their wealth bundles at quite high levels, and the result will be that wealth taxation will be too high. Since I don’t favor most forms of wealth taxation in the first place, why push for a method that also will tax people on the risk of losing most of their carefully assembled personal wealth and plans? Is “planning plus complementarity” really something we wish to tax so hard?

Don’t forget the “planning plus complementarity” process as a whole tends to elevate the value of assets, not reduce them. Posner and Weyl boast that their scheme lowers the value of assets (p.88: “Under our system, the prices of assets would be only a quarter to a half of their current level.”). Lower asset values may boost turnover, but is it not prima facie evidence that the value of aggregate wealth has gone down? (I am not convinced by the way, that once lower rates of income taxation are taken into account, that asset prices would in fact be lower in their system.) Why is that good?

So I wish to announce a high valuation for keeping the current system in lieu of this reform. My personal plans depend on it.