accounting numbers are not unique representations of the underlying constructs
they are designed to capture. It is often possible to find a vector of publicly available
information that, collectively, is highly correlated with a particular accounting number. For
example, the fair value of bank loans is a function of default risk and interest rate risk
(Barth et al. 1996). Some linear combination of book value of the loans, proxies for default
risk, and proxies for interest rate risk may be highly correlated with fair value measures,
even if those measures "perfectly" capture the underlying construct. However, a key role
of financial statements is to summarize relevant information parsimoniously and in a manner
consistent with the underlying concept. It is informative to know how well accounting
numbers play this role, even if vectors of competing proxies for the same underlying construct
exist. In fact, if the accounting number (e.g., fair value of bank loans) is capturing
the underlying construct, then we would expect other proxies for the construct (e.g., default
risk and interest rate risk) to be correlated with the accounting number. Such correlation
would indicate that the accounting number is capturing the underlying construct