1. Econometrics of Fair Values Shyam Sunder, Yale University Middle-Eastern Technical University, Department of Business Administration Ankara, Turkey, November 25, 2008

2. Sunder: Econometrics of Fair Values 2 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

3. Sunder: Econometrics of Fair Values 3 Labels Matter What is common to: –Unified Budget Act (1964, Lyndon B. Johnson) –Patriot Act (2002, George W. Bush) –Fair Values (1999, FASB)

4. Sunder: Econometrics of Fair Values 4 “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

5. Sunder: Econometrics of Fair Values 5 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

6. Sunder: Econometrics of Fair Values 6 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

7. Sunder: Econometrics of Fair Values 7 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?

8. Sunder: Econometrics of Fair Values 8 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

9. Sunder: Econometrics of Fair Values 9 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

10. Sunder: Econometrics of Fair Values 10 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)

11. Sunder: Econometrics of Fair Values 11 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)

12. Sunder: Econometrics of Fair Values 12 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)

13. Sunder: Econometrics of Fair Values 13 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

14. Sunder: Econometrics of Fair Values 14 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

15. Sunder: Econometrics of Fair Values 15 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

16. Sunder: Econometrics of Fair Values 16 Behavior of Price Movement Error with Respect to Aggregation

17. Sunder: Econometrics of Fair Values 17 Behavior of Price Measurement Error with Respect to Aggregation

18. Sunder: Econometrics of Fair Values 18 Behavior of Total (Valuation) Error with Respect to Aggregation

19. Sunder: Econometrics of Fair Values 19 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

20. Sunder: Econometrics of Fair Values 20 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

21. Sunder: Econometrics of Fair Values 21 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)

22. Sunder: Econometrics of Fair Values 22 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)

23. Sunder: Econometrics of Fair Values 23 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)

24. Sunder: Econometrics of Fair Values 24 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

25. Thank You! www.som.yale.edu/faculty/sunder Shyam.sunder@yale.edu

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