Determining the Number of Priced State Variables in the ICAPM

Suppose the ICAPM governs asset prices and there is a total of S state variables that might be of hedging concern to investors. Can it be determined which state variables are, in fact, of hedging concern? What does it mean to say that these state variables are prices, that is, that they give rise to special risk premiums in expected returns? The goal of a paper is to formulate this problem clearly and show when it can and cannot be solved. Ignoring estimation problems, it is possible to find the set of priced state variables when the state variables are identified. When the number of state variables is known, but not their names, confident conclusions about even the number of them that produce special risk premiums are probably impossible, unless the number is zero, so the ICAPM collapses to the CAPM.