It shouldn't be, anyway.
Tyler Cowen says: "These cyclically adjusted measures are useful information and should not be discarded, but I don’t wish to use them as the sole or main or dominant source of information about the stance of fiscal policy."
I'm going to make a stronger claim. One I have made before.
Consider two countries. Both countries are identical, except:
Country A has an activist government, which likes to be seen as "doing something" when there's a recession. It rushes around passing new laws increasing government spending and cutting taxes whenever there's a recession.
Country B has a lazy government, which likes the idea of "fire-and-forget" fiscal policy. It passes a law before the recession, which ensures that government spending automatically rises and taxes automatically fall whenever there's a recession. Then it goes back to sleep.
Both countries have exactly the same levels of government spending and taxes during a recession (and during a boom too).
A recession hits both countries. The accountants measure the "cyclically-adjusted deficits" ("structural deficits") in both countries. They ask "under existing tax laws and spending laws, what would the deficit be if there were no recession?" They conclude that country A has a big cyclically-adjusted deficit, and country B has none.
But there is no macroeconomic difference between the two countries.
You cannot say that country A had a good "countercyclical fiscal policy", and country B didn't. They had exactly the same fiscal policy. They just implemented it in different ways.
A second example. Country C has a strong system of automatic stabilisers, including a steeply progressive tax system, but increases tax rates in a recession. Country D has a flat tax system, but fails to cut taxes in a recession. They end up with exactly the same taxes in a recession. C has imposed "austerity", and created a 'cyclically-adjusted surplus", and D has not. But there is no macroeconomic difference between the two countries' fiscal policies. C has sinned by commission; D has sinned by omission.
"Cyclically-adjusted deficit" is a political/legal concept. It is not a macroeconomic concept.
(There might be some important macroeconomic differences between those two ways of implementing fiscal policy: maybe automatic stabilisers work more quickly than activist policies; maybe automatic stabilisers give more certainty about the future and help stabilise expectations better. But you won't see those differences captured in the cyclically-adjusted deficit number.)
Update: what should replace it? Maybe deficit/GDPgap? Or percentage deviation from a cross-country regression of deficit on GDPgap? Crude, but simple. Still vulnerable to Tyler's obection that the gap between actual and "potential" GDP is a judgement call. But better than "cyclically-adjusted deficit", which makes the same judgement call about potential GDP, and then adds a lot of legal/political noise.