Econometrics of Fair Values
Shyam Sunder
Yale University
Mid-Year Meeting of the AAA Financial
Accounting and Reporting Section
San Antonio, Tx, January 19-20, 2007
An Overview
• Language of Debate: Labels Matter
• Transforming a qualitative debate into a quantitative debate
– So we, as researchers can add value to social policy
through evidence on falsifiable propositions (beyond mere
opinions)
• A framework and results to
– View valuation methods as econometric estimators of
unobserved parameters of interest
– Choose estimators on the basis of their objective
properties, not opinions of one expert or another
– Identify key determinants of dominance between historical
and current values: degree of price instability and
magnitude of measurement errors
• Reflexivity of standards and practice in financial reporting
• Time Permitting: American Accounting Association
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Labels Matter
• What is common to:
– Unified Budget Act (1964, Lyndon B. Johnson)
– Patriot Act (2002, George W. Bush)
– Fair Values (1999, FASB)
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“Pernicious changes with
deceptively reassuring titles”
• Choose labels to put potential opponents on defensive before
the debate begins
• Oldest trick in the book of policy rhetoric
– Johnson wanted to use the social security surpluses to
finance increased spending on Great Society programs
and the Vietnam War (who can argue for non-unified
budget?)
– Bush wanted to fight the war on terror (who is against
patriotism?)
– FASB wants to use current values (who can be against fair
values in accounting?)
• “Fair” is a personal judgment, not a fact
• To avoid misuse of language, put the rhetoric of “fair” aside,
and talk about current values of which generations of
accountants and researchers have thought and written about
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The Proposal
• The price that would be received to sell an asset
or paid to transfer a liability in an orderly
transaction between market participants at the
measurement date
– Orderly transaction, not forced liquidation or a
distressed sale
– From eyes of a market participant, no entity specific
assumptions
– Highest and best use framework from the perspective
of market participants even if the acquirer has
different plans
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The Valuation Debates
• Relevance to investment decisions
• Relevance to stewardship, management of
enterprise resources, and contract
enforcement
• Other criteria for evaluation: reliability,
bias, timeliness, representational
faithfulness, cost of implementation
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Qualitative versus Quantitative
• Valuation debates have been largely been about
qualitative characteristics of rules
• Without a framework for quantified comparison,
debates can go on for ever
– People don’t change their minds
– Theories are supposed to die only with their
proponents (“science advances funeral by funeral”)
– Even that is not true in case of fair values
– Resurrection of current values under the new label
after an interval of almost 70 years
• How do we bring an element of quantified
rationality to this debate?
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Econometrics
• Great achievements of econometrics arise from our
willingness to
– Postulate an underlying structure and unknown parameters of
the problem
– Characterize the properties of alternative estimators (e.g., OLS,
GLS, 2SLS, etc.) as a function of the underlying environment
– Choose an estimator appropriate to the postulated environment
– Use data to estimate the unknown parameters, holding the
structure constant
– Examine propositions about the underlying parameter on the
basis of estimates
– Use alternative datasets of examine the propriety of assumed
structure
– When found inappropriate, change the assumed structure
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Econometrics of Valuation
• Can we use a similar strategy for documenting the
properties of valuation rules in various environments?
• It may not entirely get rid of judgments
• But still, will move the debates among valuation rules
from the domain of opinion into data
• Let me explain, starting with one postulated structure
• Remember, we can always change the postulated
structure if we find a better one later
• For now, let us focus on thinking about choice of
valuation rules as we think about choice of econometric
estimators
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Postulated Structure
• There are many resources in the economy (vector ω)
• Each firm is a special bundle of some or all of these
resources--a vector of proportions (vector w)
• Current values of resources are subject to change
over time: relative changes have a given mean
vector (μ) and covariance matrix (Σ)
• Historical costs of resources in the bundle are
known
• Relative changes in current values of the resources
are observed with an (unbiased) error term (vector ε)
which has covariance matrix (Δ)
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Two Sources of Error in Valuation
• Consider two sources of error in valuation
of a bundle of resources
– Values change over time but the valuation rule
ignores these changes (price movement
errors)
– Current values we use to revalue the bundle
are prone to errors due to imperfection and
incompleteness of markets (measurement
errors)
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Choose a Metric and Magnitude of
Errors of Valuation Rules
• Let us focus on the expected mean squared
error as the metric of errors (used in most
econometrics; we could also use bias or other
metrics)
• Magnitudes of the errors depend on
– Parameters (Δ, Σ, μ, and ω), and
– Valuation rule used to adjust historical to current
values
• The space of valuation rules is very large; even
linear subject is huge; let us just focus on the
three elements of this subset (historical cost,
general price level and current value)
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Historical Valuation
• Has price movement errors because it ignores changes
in prices from the time of acquisition to present
• The size this error (MSE) depends on parameters of the
economy:
– The mean of the vector of relative price changes (μ), and
– The covariance matrix of the vector of relative price
changes, (Σ)
• Greater the “magnitude” of these two parameters,
greater is the movement error associated with historical
valuation
• Since historical valuation ignores changes in prices, it is
free of measurement errors
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Current Valuation
• It has price measurement errors arising from
assessment of current values
• Again, the size this error (MSE) also depends on
parameters of the economy:
– If we assume that the relative changes in current values
are measured without bias (ε = 0), the MSE arising from
the mean of measurement errors is zero
– The error arises from the covariance matrix of the vector of
measurement errors in relative price changes (Δ)
• Greater the “magnitude” of this covariance matrix,
greater is the measurement error associated with current
valuation
• Since current valuation takes into account the changes
in prices, it is free of price movement errors
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General Price Level Valuation
• GPL uses a single price index to adjust historical values
towards current values
• The use of a single price index reduces the price
movement error associated with the historical estimator
but does not eliminate it
• The use of a single price index also introduces some
measurement error, although it is not as large as the
error associated with current value estimator
• The total error associated with GPL estimator depends
on the values of the parameters μ, Σ, Δ and ω.
• Let us look at the picture as a schematic graph
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Behavior of Price Movement Error
with Respect to Aggregation
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Behavior of Price Measurement
Error with Respect to Aggregation
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Behavior of Total (Valuation) Error
with Respect to Aggregation
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How Do These Estimators of Value
Perform
• Which estimator of is associated with lower mean
squared value
• It depends on the parameters of the economy
• With high price volatility and low measurement errors,
current value estimator dominates
• With low price volatility and high measurement errors,
GPL, and even historical value estimator may dominate
• In general, we should not expect that the MSE
minimizing estimator will be any of the three we have
explicitly considered
• Instead, it is likely to be some intermediate specific price
index estimator of value
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Testable Implications of Theory
• Current valuation would be more informative for
firms and industries whose
– Assets have a large mean rate of price change
– Assets have more variability in price changes
– Assets are traded in relatively perfect and complete
markets (accurately measured CV)
• Real estate, mineral deposits, films, software,
patents have large measurement errors
• Instead of cross-sectional tests (e.g., Gheyara
and Boatsman 1980, Ro 1980), we could benefit
from paying more attention to characteristics of
assets of firms and industries
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Testable Implications of Theory
• Efficient valuation rules would vary across
assets, firms and industries
• Level of aggregation at which current
values are chosen has a major impact on
the properties of valuation (left open in
FASB’s proposal)
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What Do We Learn from This
Theory?
• Theories of valuation can be integrated into a framework
to facilitate direct comparison of their properties in
specified environments
• When current prices change, and are prone to
measurement errors, neither the current nor general
price level valuation is necessarily the min(MSE)
estimator of the unobserved economic value of assets
• Generally, min (MSE) estimator is likely to be a specific
price index rule
• If the measurement errors are sufficiently large relative
to movement errors, historical cost can be the min (MSE)
estimator
• Which valuation rule has min (MSE) is a matter of
econometrics, not theory or principle (depends of relative
magnitude of parameters of the economy)
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References
• In this summary, I have drawn on the work of
many colleagues. Here are some references:
• Ijiri (Econometrica 1968), Tritschler (TAR 1969),
Sunder (JAR 1978), Hall (JAR 1982), Sunder
and Waymire (JAR 1983), Sunder and Waymire
(JAR 1984), Shriver (JAR 1986), Shriver (TAR
1987), Shih and Sunder (CAR 1987), Tippett
(ABR 1987), Lim and Sunder (JAE 1990), Lim
and Sunder (TAR 1991), Jamal and Sunder
(CAR 1995)
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Reflexivity of Financial Reporting
• In social systems, measurement is a part of a larger
cycle that cannot be ignored if we wish to understand its
properties
• If we measure because we wish to use the measures for
deciding, the choice of measurement affects decisions,
which in turn affects what we measure
• The current debate on the consequences and wisdom of
returning to current values could benefit greatly from
consideration of reflexivity
• Financial derivatives: why is it so difficult to devise
accounting for them?
– Derivatives beget standards, which beget more derivatives
– Standard setters need to consider the larger game
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American Accounting Association
• Over eight thousand members from 75 countries of the
world, each with his/her own diverse ideas, initiatives,
innovations, and energy
• It has been an eye-opener for me to learn about all the
wonderful things AAA members do
• For these few months in which you have given some of
us the privilege to hold office
• We see it as our responsibility to provide efficient shared
facilities, services and forums to make it easier you to
achieve your goals
• In this spirit, let me mention a few activities now
underway at AAA
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Internet and Ideas
• An academic organization is primarily about ideas
• As you know, Internet is bringing about radical
transformation in the way ideas, innovations and
research is disseminated, and ultimately to how it is
generated
• What does this mean for AAA as in organization?
– Aggregators, search engines, electronic publications, new
platforms, competition, intellectual property, administrative
structure and finances of the Association
• Intellectual Property & Structure Task Force (Past
President Andrew D. Bailey, Jr., chair) will submit its
interim report in Spring to help prepare us for this new,
still rapidly changing environment
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Competition of Ideas and Platforms
• AAA publishes 12 journals and 16 newsletters
• Many if not most academic disciplines are moving to
electronic platforms (even skipping print publications in
some cases)
• AAA will experiment with electronic innovations by
acquiring such a platform as a nursery for new ideas and
forums for publication, discussion, and debate
• Evolutionary (bottom up) approach to journals in contrast
to top-down command-and-control
• Let new entrants challenge the current occupants and let
the latter adjust themselves to the challenges
• Audit Section’s initiative on Current Issues in Auditing
(CIA) in electronic form as the first step; other sections?
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Global Digital Accounting Archives
Project
• Joint effort with the European and other accounting
associations (Gary Previts, Chair)
• Existence of accounting archives in many parts of the
world, some digitized
• Linking digital archives from a single Internet portal
• Identify the existence of other such archives and link
them
• Encourage digitization of accounting and business
archives
• Encourage efforts to save important archives
• Encourage discussion of, and research on, the academic
contributions of the accounting archivists in US and
abroad are doing (sessions in Chicago meetings)
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Arthur Andersen, LLP
• Glorious history of the Arthur Andersen
• Important records in their archives of great
value to researchers/historian of
accounting
• AAA Task Force to save the AAA archives
and find a university home for them when
the legal situation permits
• Effort led by Past President Arthur Wyatt
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We Academics
• It is difficult for most people in the world to understand
academics
• We spend years working on things of no apparent value to the
world
• How many of us can explain to our moms what we do with our
time, and why?
• Why do deans find so difficult to herd us cats? We teach
incentives, but are largely impervious to them
• I think it is because of imagination
• We revel in, and value, thoughts heretofore not imagined
• Thoughts change the world, even without intention to do so
• Let us assemble in Chicago in August, to revel in, and share
our imaginations
• Greg Waymire and his Program Committee is hard at work to
make it fun for us all
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See You in Chicago!
www.som.yale.edu/faculty/sunder
[email protected]