AN EXAMINATION OF SIGNIFICANT VARIABLES USED BY
COURTS IN WORTHLESS STOCK CASES
ANDREW JACKSON JUDD
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA 1985
I wish to thank John L. Kramer, Dissertation Committee
Chairman, for his editorial guidance and immediate feedback on questions that arose during the completion of this study.
Other members of my Dissertation Committee have also
made significant contributions to this research. Professors Dennis A. Calfee, John C. Henretta, and Sandra S. Kramer have freely shared their time and expertise to assist me in completing this project. Comments and suggestions from the
Ph.D. students and faculty at the University of Florida Accounting Workshop were helpful.
Finally, I wish to thank my family for encouragement, patience, and support that made completion of this project possible.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS . . . . . . . . . ii
ABSTRACT . . . . . . . . . . . v
I INTRODUCTION . . . . . . . . 1
Tax Treatment for Worthless Security Losses. 1
Significance of the Problem . . . . . 4 Research Methodology . . . . . . 8
Limitations . . . . . . . . . 16
Related Research . . . . . . . 18
Summary of Chapter Contents . . . . . 22 Notes . . . . . . . . . . 23
II HISTORICAL BACKGROUND . . . . . . 27
Statutory Provisions . . . . . . 27
Administrative Interpretations . . . . 33 Judicial Decisions . . . . . . . 33
Notes . . . . . . . . . . 39
III VARIABLE IDENTIFICATION . . . . . . 41
Data Base . . . . . . . . . 41
Research Methodology . . . . . . 42
Selection of Variables for Analysis . . . 45 Operational Definitions of Variables . . 47 Notes . . . . . . . . . . 62
IV RESEARCH METHODOLOGY . . . . . . 65
Method of Analysis . . . . . . . 65
Coding Techniques . . . . . . . 66
Coding Individual Cases . . . . . . 69
Research Question 2 . . . . . . . 71
Research Question 3 . . . . . . . 80
Research Question 4 . . . . . . . 81
Research Question 5 . . . . . . . 82
Research Question 6 . . . . . . . 83
Limitations . . . . . . . . . 85
Notes . . . . . . . . . . 86
v EMPIRICAL RESULTS . . . . . . . 88
Research Question 2 . . . . . . . 88
Research Question 3 . . . . . . . 110
Research Question 4 . . . . . . . 113
Research Question 5 . . . . . . . 118
Research Question 6 . . . . . . . 120
Comparison with Related Study . . . . 126 Notes . . . . . . . . . . 127
vi SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS . 129
Summary and Conclusions . . . . . . 131
Recommendations . . . . . . . . 138
Suggestions for Future Research . . . . 140 Note . . . . . . . . . . 141
LIST OF COURT DECISIONS ON WORTHLESS
STOCK . . . . . . . . . . 142
BIBLIOGRAPHY . . . . . . . . . . 159
BIOGRAPHICAL SKETCH . . . . . . . . 178
Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
AN EXAMINATION OF SIGNIFICANT VARIABLES USED BY
COURTS IN WORTHLESS STOCK CASES by
Andrew Jackson Judd
Chairman: John L. Kramer
Major Department: Accounting
The conditions necessary to establish that stock is worthless for purposes of loss recognition under Code
Section 165(g) are not specified in the Internal Revenue Code, Treasury Regulations, or administrative interpretations of the Internal Revenue Service (IRS). This lack of guidance has allowed taxpayers and the IRS to differ in interpreting this provision, which has frequently resulted in litigation.
The purpose of this study is to develop mathematical models that identify the significant variables used by courts in worthless stock decisions. This information may
be used by taxpayers in deciding how to resolve differences with the IRS and by tax policy-makers as a possible basis for developing provision(s) that specify conditions, which if satisfied, will qualify taxpayers for loss recognition under Code Section 165(g). Three hundred and forty-eight Tax Court and 59 Federal district court cases provided the
data used in developing separate discriminant analysis and logit models for decisions from each court.
The decision models for the Tax Court and Federal
district court decisions employed different variables. Both mathematical models were equal in their ability to predict
the outcome of Tax Court decisions but differed slightly for the Federal district court decisions.
A secondary research question in this study was to assess sensitivity of the discriminant models to the introduction of random and systematic errors in coding the variables used to construct these models. Both discriminant models were robust with respect to these types of coding errors.
Findings of this study indicate several conclusions. First, mathematical models based on variables discussed in court decisions correctly predicted more than 80 percent of these decisions. Second, the discriminant analysis and logit models were similar in their ability to predict court decisions. Third, decision models for Tax Court and Federal district court decisions employed different variables.
Fourth, discriminant models were robust with respect to the introduction of random and systematic coding errors.
Taxpayers who hold securities that have declined in
value to the point where they are worthless may deduct this loss for tax purposes, but it is not certain what a taxpayer
must demonstrate to establish that a security is worthless for tax purposes.1 This chapter presents a discussion of
the tax treatment for worthless security losses and problems that taxpayers may experience in attempting to claim a tax loss for securities that have become worthless. A research methodology is presented to provide information that may be useful in reducing the problems taxpayers may encounter in claiming a worthless security loss deduction. The limitations of this research design and related research are also presented. This chapter concludes with a summary of following chapter contents.
Tax Treatment for Worthless Security Losses
The general rule for the tax treatment of gains or losses realized from investments in securities requires
recognition (inclusion in the computation of a taxpayer's taxable income or loss for the tax year when the change in value is realized) unless otherwise provided in the
Code.2 Under this general rule, only losses that are realized by a sale or exchange can be recognized.2 Losses that would otherwise be recognized under the general rule
will be disallowed if they result from a sale to a related party defined by Code Section 267 or a "wash sale" transaction defined by Code Section 1091.4 Taxpayers holding securities that decline in value to an amount that is either less than their adjusted basis or zero incur an economic loss that is not deductible under the general rule because the loss has not been realized through a sale or exchange If securities have suffered less than a total decline in value, a taxpayer may recognize this loss through a sale or exchange of the securities with another investor who is not a related party as defined by Code Section 267.
If the securities have declined in value to the point where they are worthless, it is highly unlikely another investor could be found who would be interested in acquiring these securities. In this situation, it appears a taxpayer
would find himself in a position where an economic loss has been incurred that cannot be recognized for tax purposes.
Fortunately for taxpayers who find themselves in this situation, Congress has provided a relief provision that
allows for the recognition of losses from worthlessness sustained during the year that are not compensated by
insurance or other means.6
Code Section 165(g) deals specifically with the
deductibility of losses arising from worthless securities.
In general, this provision considers losses from worthless securities that are capital in nature and becomes worthless
during the taxable year, as a loss from the sale or exchange of a capital asset on the last day of that taxable year. Losses from the sale of securities that are not capital assets (i.e., inventory), or that are not acquired in a transaction with a profit motive do not qualify for loss recognition under Code Section 165(g).7 Losses that qualify for recognition under Section 165(g) may be classified as either long-term or short-term capital losses depending upon
the length of time they were owned prior to becoming worthless.8 Any net short-term capital loss and/or net long-term capital loss that remains after the netting process of Code Section 1222 is applied may generally be deducted up to a combined total of up to $3,000 from
ordinary income.9 Any net capital losses exceeding the $3,000 annual limit are carried forward to subsequent taxable years as either short-term or long-term capital losses.10
Initially, it would appear that Code Section 165(g) solves the loss recognition problem of taxpayers who hold securities that become worthless. However, the provision
only specifies that a deduction is available for losses incurred when securities become worthless during the taxable year. It does not specify what evidence is sufficient to establish that a security is, in fact, worthless, nor does it specify at what point in time the security became worthless.
Unfortunately, neither administrative or judicial pronouncements adequately answer the question of what
evidence definitely establishes that a security is worthless. Without any definite criteria to establish when Code Section 165(g) applies, taxpayers have nothing they can specifically rely on to refute an IRS challenge of their entitlement to loss recognition under this provision.
Without statutory, administrative, or judicial guidelines the IRS may challenge a taxpayer's claim for loss recognition under this provision regardless of the evidence a taxpayer may provide to establish the worthlessness of a security.
Significance of the Problem
If challenged by the IRS, a taxpayer's deduction for
loss recognition under Code Section 165(g) can be disallowed if the taxpayer cannot establish that worthlessness occurred in the claimed year of loss.11 Failure to establish worthlessness could obviously result in a loss of all tax benefits related to the claimed loss. However, if
worthlessness occurred in other than the claimed year of loss, the tax benefits of the loss deduction may be effected in several different ways.12
The loss could be shifted to a year closed by the
statute of limitations which would result in a total loss of the deduction. However, this outcome is not as likely as it may initially appear because Congress has replaced the
normal three-year statute of limitations with a seven-year
period for issues involving worthless securities.13 Even if the special statute of limitations can preserve a loss
deduction, it is possible for a taxpayer to lose the tax benefits of a claimed loss. This outcome may occur if, in
the year worthlessness is determined to have occurred, the taxpayer has a net operating loss or has other capital
losses that exceed the annual deduction limitation.14
Taxpayers may experience a partial reduction in the
va 1 ue of the i r tax benef i t i f the 1 oss i s sh i f ted to another taxable year. This result may occur either through a difference in marginal tax rates for the affected years, a
change in the character of the loss, or a deferral of the tax benefit of the loss to a subsequent period.
If the loss is shifted to a preceding or subsequent taxable year when the taxpayer is in a lower tax bracket, the amount of the reduction equals the amount of the loss times the change in marginal rates.15 Deferral of the loss deduction to a later taxable year causes the value of
the tax benefit to be reduced even though the taxpayer's marginal tax rate remains the same. The loss equals the
amount of the loss times the marginal tax rate times the time value of money for the period of time between the original date on which the tax benefit would have been
received and the "new" date for receiving the loss benefit. In the event that a short-term capital loss is shifted to a subsequent period where it may only be deducted as a
long-term capital loss, the value of the deduction will be reduced by fifty percent plus the lost time-value of money.16 If the taxpayer has a net long-term and/or shortterm capital loss in this subsequent taxable year, recognition of the long-term capital loss from the shifted worthless stock loss deduction may be limited by the $3,000 annual limit on deducting net long-term capital losses.
In order to eliminate these possible negative
consequences, it may occur to certain taxpayers that selling securities they consider to be worthless to a person (other than a related party subject to the provisions of Code Section 267) for a nominal amount could bring recognition of their loss under the certainty of the general gain or loss recognition rules. This strategy may not be a sound
alternative because in some cases the courts have looked through the form of this type of transaction to its substance. In doing so, they have held that Code Section
165(g) is the operative provision when worthlessness is determined to have occurred in a year other than the year of 11sale."17 Such a decision would return the taxpayer to the original problem he attempted to avoid.
The lack of guidance available to taxpayers who possess
securities that they feel have declined in value to the point they are worthless (and therefore eligible for recognition as a loss) creates a situation where affected taxpayers cannot determine with total certainty whether this deduction will be allowed. This uncertainty may lead to an
inefficient allocation of resources by both taxpayers and the IRS. Extra out-of-pocket expenses and opportunity costs could be incurred by both parties in defending different conclusions based on an identical set of facts and circumstances. In fact, the courts have even suggested that taxpayers incur such additional costs to avoid possible
challenges to their deduction. Judge Augustus Hand offered the following advice in denying a claim that he found two years too late
In cases like this the taxpayer is at times in a
difficult position in determining in what year to
claim a loss. The only safe practice, we think, is to claim a loss for the earliest year when it
may possibly be allowed and to renew the claim in
subsequent years if there is any reasonable chance
of its being applicable to the income of those
In economics literature, certainty has been identified
as one of the major attributes of ideal system of taxation.19 Accordingly, efforts directed at reducing uncertainty in our current taxation system provide a way to move a small step closer to an ideal system. Several general approaches exist for reducing uncertainty in the worthless securities area. Statutory guidance could be provided, administrative interpretations could be issued, or an improved understanding of how the courts determine worthlessness could be developed. Regardless of the form any improvement may take, an operational definition of worthlessness is required. This study seeks to identify the significant variables and to determine how they may be
combined for the purpose of providing a basis for such a definition of worthlessness.
The six major research questions to be examined in this dissertation are
Research Question 1. What variables or factors have been relevant in court decisions that have determined whether stock is worthless for purposes of loss recognition under Code Section 165(g)?
Research Question 2. Mathematically, how have the courts weighted the variables -identified in Question 1?
Research Question 3. How accurate is the model developed in answering Question 2 when compared to an heuristic model based on a synthesis of statutory provisions and court decisions?
Research Question 4. Do differences in the court of
original jurisdiction affect the accuracy of the models from Questions 2 and 3?
Research Question 5. Are the models from Questions 2 and 3 temporally stable?
Research Question 6. How sensitive is the model from Questions 2 to errors in coding the independent variables
selected for analysis?
Written court opinions that deal with loss recognition for worthless securities will be used to identify the
relevant variables. Because Code Section 165(g) mentions several different classes of securities that may be eligible for loss recognition (stock--both common and preferred, rights to subscribe to or receive stock, and debt
instruments), it is possible to identify variables that relate to all, some, or just one of these categories. Any form of combined analysis is considered inappropriate
because what may indicate worthlessness for one class of securities may not indicate the same condition for another class.
For example, in a corporate liquidation, only the
common stock would be worthless where bondholders and preferred shareholders are entitled to liquidating distributions at some future date and the common shareholders are entitled to nothing. To avoid the
inclusion of variables with possible double meanings, only one class of security--common stock--will be examined in this study. Common stock has been selected because it provides the largest set of observations from cases dealing
with loss recognition for worthless security purposes. The examination of other classes of securities may be an appropriate topic for future research.
The identification of relevant decisions through the end of calendar year 1983 was accomplished through a
combined use of the LEXIS legal research service and manual
legal research techniques.20 only those cases that were decided in a court of original jurisdiction (Tax Court, U.S. Claims Court, and Federal district courts) and not overturned by an appellate court's review were included in this study. This restriction was made to eliminate observations that were either redundant or contradictory.
Including affirming appellate decisions could result in the development of models that include the same set of variables and same finding twice for these cases but only once for nonappealed cases. Reversed decisions and related appellate decisions, if included in the construction of a model, could result in an underestimation of the importance for the variables occurring in these cases since they are not consistently associated with the court's decision. If a single case decided the worthlessness of stock for more than one company, the decisions were independently considered.
Appendix A lists all cases that were found and their respective courts of original jurisdiction. Since there were 348 decisions from the Tax Court, 59 decisions from the Federal district courts, and 8 decisions from the U.S. Claims Court, it was decided that the decisions from the
U.S. Claims Court would be deleted and that the decisions from the other two forums would be analyzed separately.
Separate analysis was selected to avoid possible nonrepresentative results in the event the Tax Court and Federal district courts use different decision models. To
determine whether the models developed in this study could be significantly influenced by fact situations related to
the stock of a single corporation, a review of the selected decisions was performed to determine how many times the
stock of a single corporation was involved in more than one decision. This review revealed only three decisions related to the stock of a single corporation which indicates approximate uniqueness in the fact situations considered by the models in this research.
Research Question 1
The relevant factors considered by the courts in
deciding loss recognition cases involving worthless securities were drawn from examination of the following sources: (1) specific factors mentioned by tax commentators and tax reporting services as indicia of worthlessness and
(2) factors not included in the preceding category that were found in the written opinions of the cases examined.
The factors compiled by this process were included in
this study only if they were mentioned in 10 percent or more of the cases. A summary of all variables that were considered for possible inclusion and the variables actually used in this study is contained in Chapter III.
Additionally, Chapter III discusses the operational definitions of, and the coding scheme used for, the
variables selected for analysis.
Research Question 2
Two different types of mathematical models will be used to determine how the courts have weighted the variables identified in Question 1 when making decisions regarding
worthlessness. First, a multiple discriminant analysis model will be developed based on the assumption that judges linearly combine the identified variables. Second, a logit analysis model will be constructed based on the alternative assumption that a non-linear combination of the identified variables may have been used by the judges. Both models will be constructed through the use of computer software packages.
Research Question 3
An heuristic model of judges' decisions regarding worthlessness will be developed by using the variables identified in Question 1. First, it will be determined by using statutory provisions and court decisions whether each variable would most likely be associated with a finding that
the security is worthless or with a finding that the security has value. Second, classification rules will be developed from the combinations of variables that would most
likely lead to a finding that the security is worthless or that it has value.
The relative accuracy of the quantitative model
developed in Question 2 and the heuristic model developed in
Question 3 will be calculated by determining the classification accuracy of each model. For the heuristic model, the classification accuracy will be determined by dividing the number of correctly classified decisions by the
number of actual decisions. The classification accuracy of the quantitative model will similarly be calculated, but with some minor modifications. Since the heuristic model
wi 11 be developed without the use of any of the characteristics of the population being considered, it will
be possible to directly calculate its classification accuracy. However, since the quantitative models will be developed from the population of decisions, alternative procedures were necessary to avoid classification accuracy figures that indicate the models' ability to classify
themselves instead of decisions not used in constructing these models.
Accordingly, classification accuracy of the
quantitative models will be tested by the use of two different methods. For the 348 Tax Court decisions, a
holdout sample will be used. The use of a holdout sample for Federal district court cases will not be possible because of the small population size (only 59 decisions). To test the classification accuracy of the Federal district
court model, a jackknife validation procedure will be used. In this procedure, a discriminant function will be
calculated for n 1 decisions, where n is equal to the number of decisions in the population. This n 1
discriminant function will then be used to classify the omitted decision. This process will be repeated n 1 times and the number of correctly classified decisions will be used as an estimate of the model's classification accuracy.
Research Question 4
To determine whether different decision models were
used in the Tax Court and Federal district courts, a model based on all decisions made by the Tax Court will be used to predict the outcome of decisions made in the Federal district courts and a model based on all of the Federal
district court decisions will be used to predict the Tax Court decisions. The classification accuracy of the Federal district court decisions predicted by using the Tax Court
-model will then be compared with the classification accuracy of the Federal district court model when it is applied to Federal district court decisions. A comparison of the
classification accuracies of the Tax Court decisions will be made in the same manner. Additionally, component variables in each model will be analyzed for possible differences.
Research Question 5
The temporal stability of the models will be tested in two ways. First, classification functions will be developed by using the first one-half of the decisions to classify the outcome of the second one-half of the decisions. Since
there are only 59 Federal district court decisions they will not be considered in answering this question because further
reduction of such a small population would most likely result in statistically invalid models. The first one-half of the Tax Court decisions made between 1921 and 1940 will
be used to predict the second one-half of the loss decisions made between 1941 and 1983. Second, to assess the current
validity of the models, their classification accuracy will be calculated and examined for differences when applied to the earliest 90 percent of the decisions and the most recent
10 percent. Again, only Tax Court decisions will be considered because of the relatively small population of Federal district court decisions.
Research Question 6
To determine how the models may be affected by errors in the coding of the independent variables, two types of errors will be considered. To assess sensitivity of the models to the introduction of random errors, the data being
analyzed in this study will be modified by the introduction of random error to between 3 percent and 10 percent of the observations. The models developed from the data containing
these random errors will be compared with models based on data not containing these introduced errors for differences
in the weighting of individual variables and overall classification accuracy. Sensitivity to the introduction of
systematic coding errors will be examined by comparing
models that have had the coding of the two most significant
variables changed with models having unchanged coding for differences in variable weighting and classification accuracy.
The findings of this research may be affected by more than uncertainty regarding the appropriateness of various statistical and mathematical assumptions than have been made. Several conditions may result in differences between the factors actually considered by judges and the factors this research has associated with their decisions.
First, in tax litigation the burden of proof is placed on the taxpayer to demonstrate the IRS's position is
invalid.21 The application of this principle resulted in differing conclusions in three cases all of which dealt with
the worthlessness of middle West Utilities Company's common stock in 1932. Based on the information provided by the
taxpayer in George H. Horning, the Board of Tax Appeals did 22
not find the stock worthless in 1932. However, based on different information presented by the taxpayers in
Mary S. Peabody and Benjamin Mahler, the same court concluded that the common stock had become worthless in 1932.23 Had these cases been decided in the reverse order, the court would have been aware of additional information that it could not cite as a basis for its decision.
Second, judges' written opinions may not include all variables presented for consideration since these opinions are not verbatim trial records. If a judge includes discussion of enough significant variables to justify his finding to a possible appellate review, he may not feel that it is necessary to discuss the factors he considers insignificant.
Third, it is possible that individual biases of the researcher may have resulted in the miscoding of some variables. To minimize the possibility of this type of error, 10 percent of the decisions were coded independently and compared with the original coding. Less than 1 percent of the originally coded variables were found to be incorrect. The nature of the-coding errors were examined and found to be nonsystematic. The errors were then corrected. If this error rate is representative, the effect
of individual coding bias on the results of this study should only be minimal, if measurable at all. Relevant to this assumption is the research of Pollard and Copeland. Their study found that introduction of a 3 percent error rate only reduced the classification accuracy of a
discriminant model predicting the outcome of "tax home" cases by 2 percent.24
A final limitation to this study is found in the nature of the decisions themselves. Assuming that both taxpayers
and the IRS would litigate the question of worthlessness only if each felt they had a good chance of winning, a number of disputes between these two parties, that were not
litigated but were instead settled by compromise, have been eliminated from consideration. Accordingly, the results of this study may not be generalizable to all issues involving the worthlessness question.
This study has links with prior research efforts that have used mathematical models to describe both judicial and
nonjudicial classification decisions. The research design of this dissertation is primarily based on political science research, where the use of mathematical models to describe the judicial decision process originated, and tax-oriented
accounting research, which has specifically applied this approach to the analysis of tax decisions. Other accounting
research that has used mathematical models to describe nonjudicial decisions indicates this methodology is desirable for more reasons than its application in similar studies.
Mathematical Techniques in Judicial Decision Research
Political science research. The first research to use mathematical modeling to analyze judicial decisions was a
1957 study by Kort that examined right to counsel decisions made by the Supreme Court.25 He assigned numerical values to factors mentioned by the judges and then summed these
values to obtain a score for each case to predict the court's decision. In 1963, Kort refined this technique by
using factor analysis to reduce the number of independent
variables in his model. These independent variables were used to predict case outcomes through the use of a multiple regression model.26
In a subsequent study, Nagel used correlation analysis to predict the outcome of reapportionment cases.27 In this study, Nagel suggested using discriminant analysis to analyze binary judicial decisions. Ulmer published the first research using discriminant analysis when he examined the voting behavior of Judge Felix Frankfurter in Supreme Court cases involving civil liberties issues.28
Tax research. Accountants have used mathematical models to analyze two major aspects of tax decisions.
First, mathematical models have been used to determine the significance of factors contained in Treasury Regulations or
binding appellate court decisions in tax decisions. Representative of this approach is Englebrecht and Rolfe's use of discriminant analysis to determine the significance
of factors contained in the U.S. Supreme Court's decision in U.S. v. Davis on subsequent court decisions involving dividend equivalence in stock redemption issues.29 Second, in areas where no specific guidelines have been developed for the courts to follow, tax researchers have used mathematical models to determine which factors have the greatest ability to predict the past behavior of the courts. This technique was applied by Stewart who used discriminant analysis and logit analysis to determine the factors
employed by federal courts in deciding employee versus independent contractor issues.30
Directly related to this research is a study by
Kilpatrick that used both discriminant analysis and logit analysis to model the Tax Court's decision process in eightfour cases involving worthless stock issues.31 In his 1984 study, a discriminant function using Insolvency Occurring During the Claim Year, Discontinuation of operations During
the Claim Year, Dissolution of the Company During the Claim Year, Bankruptcy Filed After the Claim Year, and Insolvency After the Claim Year as independent variables correctly predicted the outcome for 88.1 percent of the cases. Using
the same set of independent variables a logit function correctly predicted 86.9 percent of the decisions. Also, temporal stability of the models was indicated. This study
will differ from Kilpatrick's research in several major ways. First, the population of all Tax Court cases will be examined versus a sample of eighty-four. Second, Federal
district court cases will also be examined. Third, an heuristic model is to be developed for comparison purposes. Fourth, the sensitivity of the models developed in this study will be examined with respect to the introduction of coding errors.
Multiple discriminant analysis and logit analysis have been used in financial accounting research to study the
relationship between selected financial ratios and business failure. Libby's work in this area has implications relevant to this study.32 First, multiple discriminant analysis was used to describe how loan officers used financial ratios to predict bankruptcy, which indicates this technique has also been considered appropriate in the analysis of nonjudicial decisions. Second, but more importantly, the selection of discriminant analysis was justified, not only for its ability to accommodate binary dependent variables, but also for its compatability with psychological theory of decision making. L ibby's theoretical justification is based on the ability of
discriminant analysis to apply Brunswik's "lens model" in an experimental setting.3 The lens model's major postulate is that environmental conditions are known to decision makers
only in the form of cues related to those conditions and that the decision maker must weigh, assess, and combine
these cues to predict the actual environmental conditions. Libby linked Brunswik's lens model to discriminant analysis through the ability of discriminant analysis to explain
decision maker's predictions (discrete dependent variables) with a linear combination of environmental causes
A quantitative model, conceptually identical to the lens model, has been developed by Jensen and Horvitz to describe the judicial decision process.34 Jensen and Horvitz's model relates judicial decisions to fact situations through weights judges assign to individual facts
in their legal reasoning process. This model is based on the concepts of ratio decidendi, the reasoning process used
by judges to apply rules of law to fact situations in cases they hear, and stare decisis, consistent application of the law by judges, both individually and collectively, in similar fact situations. The distinction between Jensen and
Horvitz's judicial decision model and Brunswik's lens model is that Jensen and Horvitz's model addresses how individuals process information related to unknown events and Brunswik's model addresses how individuals process information related to known events.
These two models that explain decisions as a weighted combination of variables upon which decisions may be based
provide theoretical support for the use of discriminant analysis in this research.
Sununary of Chapter Contents
This study is divided into six chapters. Chapter I is the introduction to the study which includes a description of the nature and significance of the problem, the research questions selected to examine this problem, the basic
research methodology that will be used, and the possible limitations of the study.
Chapter II provides a historical perspective of the statutory provisions and judicial decisions affecting the determination of whether or not a security is worthless for purposes of loss recognition.
Chapter III presents and applies the research
methodology used to identify the variables of interest in this study which is the objective of Research Question 1.
Chapter IV contains a detailed outline of the research methodology selected to examine Research Questions 2 through 6.
Chapter V presents the models developed to describe the courts' decision-making behavior in answering Research Questions 2 through 6. Differences and similarities among these models are identified and evaluated.
Chapter VI summarizes the preceding chapters, discusses the implications of this study, and presents recommendations for future research.
lCode Section 165(g). All references are to the Internal Revenue Code of 1954 unless otherwise noted.
2Code Sections 1001(c) and 61(3).
3Code Section 1001(c).
4Code Section 267(b) specifies nine categories of
related parties for which losses incurred on transactions
involving these related parties are disallowed. Code Section 1091 generally defines a "wash sale" as sale in which a loss is realized but where substantially identical securities are acquired during either the 30-day period
preceding or following the date of sale that permits the taxpayer to retain relatively the same economic position.
5Code Section 1001(c).
6Code Section 165(a).
7Code Section 1221 and Code Section 165(c).
SCode Section 1222(2) defines a short-term capital loss as a loss from the sale or exchange of a capital asset held for less than 6 months and Code Section 1222(4) defines a long-term capital loss as a loss from the sale or exchange of a capital asset held for more than 6 months.
9Code Section 1211(b) provides that net short-term capital losses be deducted first on a dollar-for-dollar basis and one-half of any net long-term capital losses may be deducted in reaching the $3,000 annual limit.
10Code Section 1212(b).
11Code Section 7453 and Tax Court Rule of Practice 32 place the burden of proof on the taxpayer.
12Since the primary role of the IRS is to collect
revenues for the government, it is assumed the IRS would not challenge an incorrect position taken by a taxpayer, that if corrected, would result in a refund. Accordingly, only negative consequences will be considered in this study.
13Code Sections 6511 (a) and 6511(d) (1).
14Generally, Code Section 1211 allows noncorporate
taxpayers up to a $3,000 deduction for capital losses that exceed capital gains. Corporate taxpayers may only deduct capital losses to the extent they do not exceed capital gains.
151t is unlikely for the IRS to attempt to shift a
deduction to a taxable year when the taxpayer has a higher marginal tax rate or to an earlier year that is not closed by the statute of limitations. However, if the taxpayer has
a lower marginal tax rate in the earlier year, the IRS may attempt to shift the deduction to that earlier year.
16Code Section 1211(b).
17Grant B. Shipley, 17 TC 740 (1951) and Frank C. Rand, 40 BTA 233 (1941).
18Minnie K. Young v. Commissioner, 123 F.2d 597 (CA-2, 1941).
19G.P Break and J.A. Pechman, Federal Tax Reform: The Impossible Dream (Washington, D.C.: Brookings Institution, 1975).
20LEXIS, a service of Mead Data Central, is a legal
reference system that stores the texts of a large number of court cases in a computer accessible form. This system can
provide a researcher with anything from a case cite to the complete text of any case (stored in the system) that
contains key words or phrases selected by the researcher. LEXIS stores Board of Tax Appeals and Tax Court decisions
issued since 1924, Tax Court Memorandum decisions since 1942, District Court decisions since 1960, and U.S. Claims Court decisions since 1942. manual research techniques were used to identify cases not stored by LEXIS.
21-Code Section 7453 and Tax Court Rule of Practice 32 place the burden of proof on the taxpayer.
22George H. Horning, 35 BTA 897 (1937).
23Mary S. Peabody, 38 BTA 1086 (1938) and Benjamin Mahler, P-H BTA Memo Dec. 39,468 (1939).
24W.B. Pollard and R.M. Copeland, "Evaluating the
Robustness of Multivariate Tax Models: A Section 162 (a) (2) model" (unpublished manuscript, 1984).
25F. Kort, "Predicting Supreme Court Decisions
Mathematical ly: A Quantitative Analysis of the 'Right to Counsel' Cases," 51 American Political Science Review 1 (1957).
26F. Kort, "Content Analysis of Judicial Opinions and Rules of Law," in Judicial Decision-Making (New York: Free Press of Glencoe, 1963).
27 S.S. Nagel, "Applying Correlation Analysis to Case Prediction," 42 Texas Law Review 1066 (1964).
28..Ulmer, "The Discriminant Function and a
Theoretical Context for Its Use in Estimating the Votes of Judges," in Frontiers of Judicial Research (New York: J. Wiley, 1968).
29T.D. Englebrecht and R.J. Rolfe, "An Empirical Inquiry into the Judicial Determination of Dividend Equivalence in Stock Redemptions," 4(l) 'Journal of the American Taxation Association 19 (1982).
30D.N. Stewart, Employee or Independent Contractor: An Examination of the Relevant Variables Employed by the Federal Courts in Deciding the Question (Ph.D. dissertation, University of Florida, 1980).
31B.G. Kilpatrick, The Determination of Worthless
Securities Under Internal Revenue Code Sec. 165(g): Empirical
Evidence from Judicial Decisions (Ph.D. dissertation, Oklahoma State University, 1984).
32R. Libby, "Accounting Ratios and the Prediction of Failure: Some Behavioral Evidence," 13(l) Journal of Accounting Research 150 (1975).
33E. Brunswik, The Conceptual Framework of Psychology (Chicago: University of Chicago Press, 1952).
34H.L. Jensen and J.S. Horvitz, "A Theoretical Framework for Quantifying Legal Decisions", 20(1) Jurimetrics Journal 121 (1979).
This chapter presents a survey of statutory provisions, administrative interpretations, and judicial decisions related to the deductibility of worthless security losses.
The Tariff Act of October 3, 1913, which introduced
the first constitutionally valid federal tax on income, did not specifically allow a deduction for worthless securities. Instead, the Act allowed a deduction for losses in general, which included worthless security losses. Section II.B of this Act allowed individuals to deduct
losses actually sustained during the year, that
were not compensated for by insurance or
otherwise, in computing net income subject to tax
so long as these losses were incurred in a trade
or arose from fire, storm, or shipwreck.
Corporations were also allowed to deduct uncompensated losses. However no restrictions on trade or casualty loss deductions applied.1
The Revenue Act of 1916 expanded the scope of losses
that individuals could deduct by providing for the deductibility of
losses not connected with a trade or business, but
entered into for profit to the extent of profits
Additionally, this Act limited both individual and corporate loss deductions related to property held on March 1, 1913, to the fair market value of the property on that date.3
The general loss deduction provisions were again
modified by the Revenue Act of 1918. This Act removed the "to the extent of profits therefrom" restriction that had
applied to losses incurred in transactions entered into for profit, but not connected with a trade or business
The next change to effect the general loss deduction
provisions occurred in the Revenue Act of 1934. The nature of what was deductible did not change, but the potential amount of the deduction was affected by the Act's limitation
on the deductibility of capital losses.5 Since most investors hold securities as capital assets, this change was of considerable importance. Commenting on this change in
the deductibility of capital losses, the House Ways and Means Committee stated
This provision is an important part of the new policy recommended for the treatment of capital
gains and losses from the sale or exchange of
property, as already described. It makes clear
that individuals and corporations are entitled to
deduct capital losses only to the extent of
The Revenue Act of 1934 also provided special treatment for worthless security losses. Since worthlessness does not occur through a sale or exchange, losses of this nature (even though related to capital assets) were deductible without regard to capital loss limitations. This exclusion of worthless securities losses from the capital loss
limitation provisions of the 1934 Act was not changed by the
Revenue Act of 1936.7 This exclusion from the capital loss
limitations was finally eliminated by the Revenue Act of
1938. In explaining this change, the House Ways and Means
Committee offered the following explanation
Under Section 23(e) of the Revenue Act of 1936 a loss sustained from securities becoming worthless
which is deductible under that subsection is
deductible in full and against ordinary income.
In contrast thereto a loss sustained from the sale
or exchange of such securities as are capital
assets is not only subject to reduction by the
percentage brackets of section 117(a) or that Act
but can not be offset against ordinary income
except to the extent of $2,000. This distinction in treatment is not satisfactory, since, in either
case, the loss sustained by the taxpayer is a loss
of capital and consequently should be treated
similarly for tax purposes. This difference in
treatment is eliminated by the bill. Section
23(g) thereof, dealing with capital losses,
subjects losses arising from stock or stock rights
becoming worthless to the same limitations
provided under section 117 of the bill with
respect to sales or exchanges.8
The Revenue Act of 1938 used two separate sections to
provide constructive sale or exchange treatment for
securities becoming worthless during a taxable year.
Section 23(g) was enacted to provide this treatment for
equity securities and Section 23(k) was enacted to provide
this treatment for debt securities. Section 23(g) contained
the following wording:
(g) CAPITAL LOSSES.-(1) LIMITATION.--Losses from sales or exchanges of capital assets shall be allowed only to the extent
provided in Section 117.
(2) SECURITIES BECOMING WORTHLESS.--If any
securities (as defined in paragraph 3 of this
subsection) become worthless during the taxable year and are capital assets, the loss resulting
therefrom shall, for the purposes of this title,
be considered as a loss from the sale or exchange,
on the last day of such taxable year, of capital
(3) DEFINITION OF SECURITIES.--As used in this
subsection the term "securities" means (A) shares
of stock in a corporation, and (B) rights to
subscribe for or to receive such shares.
Section 23(k) contained similar wording but applied to securities defined as
bonds, debentures, notes, or certificates, or
other evidences of indebtedness, issued by any
corporation (including those issued by a
government or political subdivision thereof), with
interest coupons or in registered form.9
These two sections were included, unchanged, in the
Internal Revenue Code of 1939.10 Additions to these two Code Sections made by the Internal Revenue Act of 1942 were the last major changes to affect the deductibility of losses from worthless securities. Sections 23 (g) (4) and 23 W (5) allowed corporations to deduct losses from worthless securities of certain affiliated corporations as ordinary losses.11 The combining of Sections 23(g) and 23(k) to form Code Section 165(g) of the Internal Revenue Code of 1954 resulted in the provision that currently specifies the treatment of losses from worthless securities.
In its current form, Code Section 165(g)(1) allows a taxpayer to treat the loss from a security that becomes
worthless on any date during the taxable year as a loss from the sale or exchange of a capital asset on the last day of the taxable year. Exceptions occur in the case of securities that are not held as capital assets or securities
that qualify for other than capital asset treatment. In the former category are securities held as inventory by a securities dealer or securities acquired in a transaction without a profit motive.12 The latter category consists of affiliated bank stock described in Code Section 582(b), securities of subsidiary corporations described in Code
Section 165(g)(3), Small Business Investment Company Stock, and Small Business Corporation Stock described in Code Sections 1242, 1243, and 1244.
The securities eligible for loss recognition under Code
Section 165(g) are of the following types described in Code Section 165 (g) (2)
(a) A share of stock in a corporation;
(b) A right to subscribe for, or to receive, a
share of stock in a corporation; or
(c) A bond, debenture, note or certificate or
other evidence of indebtedness, issued by a
corporation or by a government or a political
subdivision thereof, with interest coupons or in
Since the Code only deals with the treatment of losses from securities that become worthless and specification of
securities eligible for this treatment, the Treasury Regulations need to be examined to determine what, if any, conditions must be satisfied to establish that a security is worthless in the claimed year of loss to qualify for loss recognition under Code Section 165(g).
Treasury Regulation Section 1.165-4 which addresses the decline in value of stock provides a partial answer to the question of how to determine when a security becomes
worthless by indicating the following conditions that do not indicate worthlessness
No deduction shall be allowed under Section 165(a)
solely on account of a decline in the value of stock
owned by the taxpayer when the decline is due to a fluctuation in the market price of the stock or to
other similar cause. A mere shrinkage in the
value of stock owned by the taxpayer, even though extensive, does not give rise to a deduction under
Section 165(a) if the stock has any recognizable
value on the date claimed as the date of loss.
Although this Regulation Section specifically refers to Code Section 165(a) it also applies equally to Code Section 165(g) since Code Section 165(a) is the operative provision allowing the deduction of losses in general and Code Section
165(g) refers to a specific type of loss deductible under Code Section 165(a). The guidance provided by this Regulation Section is only conceptual in nature since it fails to specify what is required to demonstrate that recognizable value does or does not exist.
The only other portion of the Regulations directly
related to Code Section 165(g) is Section 1.165-5 which specifically addresses worthless securities. This Regulation Section is primarily a restatement of Code
Section 165(g) and is totally silent with regard to determining if and when a security becomes worthless. This lack of statutory guidance to determine when the requisite
state and date of worthlessness conditions have been satisfied makes it necessary for taxpayers to refer to other authoritative sources for possible answers.
Pronouncements of the IRS do not carry the same
authority as the Internal Revenue Code or Treasury Regulations, but they may be a potential source of guidance for taxpayers since they can communicate conditions the IRS
will consider in deciding whether to accept or challenge a taxpayer's position regarding the application of an ambiguous statute. Currently, no IRS Revenue Ruling or IRS Revenue Procedure specifies conditions taxpayers may rely on
to determine how the IRS wi 11 respond to a claim for loss recognition under Code Section 165(g). In addition to
public silence, the IRS has not internally communicated a position on this subject to its own personnel. The IRS Audit Guidelines only mention worthless securities as a potential area for investigation, but do not specify the
conditions that may lead to an IRS challenge of a taxpayer's deduction for worthless securities.13 Also, a search through tax reporting services and LEXIS did not indicate
the existence of any General Counsel's Memoranda, Technical Memoranda, or Actions on Decisions expressing an IRS position on Code Section 165(g) issues.
When both statutory and administrative sources fail to adequately define the terms used in the Code, taxpayers and
the IRS may arrive at different conclusions regarding the
same set of facts and circumstances. These differing
conclusions, should they occur, may be resolved through mutual agreement. In the event an agreement cannot be
reached, then litigation usually occurs. Because taxpayers have no public access to compromise-type agreements between
the IRS and taxpayers, written court opinions involving tax issues constitute the primary source of information taxpayers may use to predict the most likely resolution of a difference with the IRS.
Accurate prediction is often possible when a study of written opinions concerning the application of a specific provision indicates that judges have almost consistently used a single decision process in reaching their conclusions. This potential predictability, of course, rests on the assumption that decision patterns exhibited in
the past wi 11 continue to be appl ied in the f uture. This may not be an unrealistic assumption if judges follow the decision process introduced in a prior case because it represents a comprehensive and sound legal approach to
resolving the issue or the decision process is specified in a binding appellate court decision. The results of empirical research by Boyd and Englebrecht and Rolfe support
this assumption.14 Boyd found that lower courts generally followed the Sixth Circuit Court of Appeals' decision in the Mason Manufacturing Co. case in resolving reasonableness of compensation issues for closely held corporations. Englebrecht and Rolfe found a similar relationship between
the Supreme Court's decision in the Davis case and subsequent lower court decisions regarding dividend
equivalence in stock redemption cases. However, if such a judicial precedent does not exist with respect to the resolution of an issue, judges are free to adopt any decision process they deem appropriate.
Cases involving loss recognition under Code Section
165(g) fall somewhere between these two extremes, so their analysis may be of some value in assessing potential court behavior. No specific decision rule has been consistently
followed by the courts, but a general approach has been used that provides more guidance than is available from either statutory or administrative sources.
In resolving issues that require the determination of
worthlessness, the courts have generally held that corporate liabilities must exceed corporate assets and no change in
this condition will occur in the foreseeable future.15 These two conditions have been satisfied when, in the opinion of the court, the taxpayer can demonstrate that the security is worthless in the claimed year of loss and that
it had value in the preceding taxable year.16
In Morton v. Commissioner, the Board of Tax Appeals
discussed its use of an approach to simultaneously establish when the loss of both current and future value occurred.17 This approach was based on the search for an "identifiable
event" having negative financial implications so large that it caused the loss of both current and future value for the
stock in question. The following explanation of this approach was provided by the court
stock may not be considered as worthless even when
having no liquidating value if there is a
reasonable hope and expectation that it will
become valuable at some future time, and that such
hope and expectation may be foreclosed by the
happening of certain events such as bankruptcy,
cessation from doing business, or liquidation of the corporation, or the appointment of a receiver
for it. Such events are called identifiable in that they are likely to be immediately known by
everyone having an interest by way of stockholding
or otherwise in the affairs of the corporation;
but regardless of the adjective used to describe
them, they are important for tax purposes because
they limit or destroy the potential value of the
Since a large number of potential identifiable events
and combinations thereof exist, it is possible that, because
of differences in individual facts and circumstances among cases, the event(s) that courts regard as being "identifiable" in one case may not be so regarded in other cases. For example, in Foster v. Commissioner, the stock of a bank that became insolvent in 1933, and which did not liquidate until 1934, was found by the court to have become worthless in 1933.19 However in Nelson v. United States the stock of a corporation that became insolvent in 1931, and continued operations at a minimum level until 1935 when it was forced into liquidation by creditors, was determined to
have become worthless in the year of dissolution.20 While these cases may be distinguished from each other because of continued operations in only one case, they are evidence that one cannot rely on the simple occurrence of an event that has been regarded as "identifiable" in one case to
predict the outcome of another case when that same event also occurs.
In addition to dealing with differences in facts and
circumstances when determining whether an event is identifiable, the courts have also had to determine which event will be defined as the identifiable event in situations where more than one event has occurred and these events relate to different taxable years. Primarily, this
problem involves the relative importance of the opinion and actions of the taxpayer (versus other events). At one extreme is reliance on the subjective opinion and actions of the taxpayer that was taken by the Second Circuit Court of Appeals in Smith v. Helvering.21 In this case the court held that the stock of a corporation that had ceased to do any significant amount of business, other than to make casual sales on orders received after 1929 (the year when most of its assets were sold), did not become worthless until 1937 when it filed for a certificate of dissolution. The court based its finding of remaining value in the corporation on the fact that the taxpayer continued to advance funds to the corporation which, for the most part,
were used to pay corporate obligations the taxpayer had guaranteed. In overturning the decision of the Board of Tax
Appeals which found that the stock had become worthless in 1929, this court stated
The test applied by the Board was stated in
the following terms: "The loss must be taken in
the year in which it sustained and at no other
time and this means the year in which these shares
in every substantial and realistic way became worthless. We think the decision of the Board
too severely restricted the taxpayer and sets too high a standard of industrial performance;
especially in the light of the remarkable industrial developments often achieved by
courageous and optimistic American businessmen,
who refused to be dissuaded when bankers
and other conservative citizens advised that
their enterprises were worthless in "every
substantial and realistic way." Henry Ford is
a striking example. Even though, perhaps, a
businessman should not be encouraged to be an
incurable optimist, if he is one, nevertheless,
and continues to express his optimism by putting
money into an insolvent organization, he should
be given the benefit of the doubt.22
In Boehm v. Commissioner the Supreme Court, when
confronted with this issue, reached a different
conclusion.23 This court placed much less weight on the
opinion and actions of the taxpayer in deciding whether the
stock of a corporation that went into receivership in 1932
became worthless during that year, or during 1937 when a suit
brought against the officers of the corporation by the
taxpayer and other shareholders was settled for a nominal
amount. In reaching this conclusion, the court stated
determination of whether a loss was in fact
sustained in a particular year cannot fairly be
made by confining the tier of facts to an
examination of the taxpayer's beliefs and actions.
Such an issue of necessity requires a practical
approach, all pertinent facts and circumstances
being open to inspection and consideration
regardless of their objective or subjective
nature. As this Court said in Lucas v. American Code Co., 280 U.S. 445, 449, 50 S. Ct. 202, 203, 74 L. Ed. 538, 67 A.L.R. 1010, "no definite legal
test is provided by the statute for the
determination of the year in which the loss is to be deducted. The general requirement that losses
be deducted in the year in which they are
sustained calls for a practical, not a legal,
The standard for determining the year for
deduction of a loss is thus a flexible, practical
one, varying according to the circumstances of
each case. The taxpayer's attitude and conduct are not to be ignored, but to codify them as the decisive factor in every case is to surround the
clear language of Section 23(e) and the Treasury interpretations with an atmosphere of unreality
and to impose g~jve obstacles to efficient tax
While the Supreme Court may have resolved the issue of the relative weights attributable to subjective versus objective events, no court has yet developed a scheme to assign relative weights to different objective events that may occur in different taxable years. This lack of guidance to determine which event will be regarded as being
"identifiable" results in an environment of uncertainty for taxpayers trying to assess how the courts may resolve a difference with the IRS regarding the worthlessness of a particular stock.
'Tariff Act of October 3, 1913, Section II.G(b), 38 Stat. 114 (1913).
2Revenue Act of 1916, Section 5(a) Fifth, 39 Stat. 756 (1916).
3dSection 5(a) Fourth, and Section 12(a) Second.
4Revenue Act of 1918, Section 214(a)(5), 40 Stat. 1057 (1918).
5Revenue Act of 1934, Section 23(j), 48 Stat. 680 (1934).
61nternal Revenue Bulletin 1939-1 C.B. 571.
7Revenue Act of 1936, Section 23(e), 49 Stat. 1648 (1936).
8Internal Revenue Bulletin 1939-1 C.B. 741.
9Revenue Act of 1938, Sections 23(9) and 23(k)(3), 52 Stat. 447 (1938).
10Code Sections 23(g) and 23(k) of the Internal Revenue Code of 1939.
llRevenue Act of 1942, Sections 112 and 113, 56 Stat. 798 (1942).
12Code Sections 1236 and 165(c).
13Internal Revenue Service, Internal Revenue Manual (Chicago: Commerce Clearing House, 1984), pp. 8169-70.
14J. Boyd, Validation of Guidelines for Determining Reasonable Compensation in Closely Held Corporations
(Ph.D. dissertation, University of South Carolina, 1977); and T.D. Englebrecht and R.J. Rolfe, "An Empirical Inquiry into the Determination of Dividend Equivalence in Stock
Redemptions," 4(1) The Journal of the American Taxation Association 19 (1982).
15William A. Sipperell, TC Memo 1962-92 (1962), Andrew Popovich, TC Memo 1965-174 (1965), and Norman B. Jacobwitz, TC Memo 1968-261 (1968).
16Commissioner v. George Whitney, 169 F.2d 562 (CA-2,
1948), James G. Hoover, 32 TC 618 (1959), and Burt Ruud, TC Memo 1969-252 (1969).
17Sterling Morton, 38 BTA 1270 (1938).
19W.N. Foster v. Commissioner, 112 F.2d 109 (CA-1, 1940).
20Norman Nelson v. U.S., 131 F.2d 301 (CA-8, 1942).
21Herbert W. Smith v. Helvering, 141 F.2d 529 (CA-D.C., 1944).
23Lillian Boehm v. Commissioner, 326 U.S. 287 (1945).
This chapter identifies the cases and variables
selected for analysis in answering Research Question 1. Operational definitions for each variable and the context in which these variables have been discussed in court decisions are presented. Additionally, frequencies of occurrence in Tax Court and Federal district court decisions are presented
for those variables found in 10 percent or more of the cases selected for analysis.
Preparation of the data base first required the
identification of all relevant cases. Case identification was accomplished through a combination of the LEXIS legal research service and manual research techniques. This study only considers decisions from courts of original
jurisdiction (Tax Court, Federal district courts, or the U.S. Claims Court) that were not overturned by an appellate decision. Affirming appellate decisions were excluded to prevent double-weighting the same set of variables. Reversed decisions from the court of original jurisdiction were eliminated to exclude nonbinding decisions. Reversing
appellate decisions were eliminated since they include a variable not present in decisions from courts of original
jurisdiction--specifically, the opinion from the court of original jurisdiction. Appendix A indicates all decisions rendered through December 31, 1983, satisfying the above inclusion criteria. The distribution of these decisions among the various courts is
Court Number of Decisions
Tax Court 348
Federal district courts 59
U.S. Claims Court 8
In addition to determining the cases that would be
analyzed in this study, it was also necessary to decide how LThese cases would be analyzed. Since one of the research objectives of this study is to determine if differing decision processes are used by the various courts, it was
decided that the decisions from each forum would be separately analyzed. Because only 8 of the 415 decisions were mnade by the U.S. Claims Court, these decisions were eliminated from analysis since it is highly unlikely a statistically valid model could be developed from so few observations.
The identification of variables used by courts in worthless stock decisions was accomplished through a
two-step process. First, the following tax literature was reviewed to identify those variables other researchers have regarded as significant in the determination of
worthlessness: Commerce Clearing House's Standard Federal Tax Reports,1 Mertens Law of Federal Income Taain2 Prentice Hall's, Federal Taxes,3 Research Institute of
America's Federal Tax Coordinator 2d,4 Tax Management Portfolio No. 96 3rd,5 and an article entitled "Stock Losses: Establishing Worth lessness."6 Second, actual court decisions were reviewed to determine if the courts considered variables that had not been mentioned in the tax literature.
Since each source had its own unique way of describing
variables relevant to the determination of worthlessness, it was necessary to combine variables that were conceptually similar but described differently. This combination process
resulted in the development of the following variables and, if applicable, related subcategories:
6. Operating Losses.
7. Internal (Corporate and Shareholder) Actions and
a. Continued business operations.
b. Market conditions for principal product(s).
c. Value of principal assets.
d. Renewal or surrender of corporate charter.
e. Contributions of additional capital.
f. Proceeds from sales of stock.
g. Opinions regarding future profitability.
h. Sale of corporate assets.
i. Sale of firm.
j. willingness to sell shares of stock.
k. Willingness to sell corporate assets.
1. Shareholder confidence in management.
M. Attempts to acquire additional outside capital.
8. External (Third Party) Actions and Testimony:
a. Marketability of the corporation's stock.
b. Reaction to efforts by the firm to obtain
C. Reaction to changes in the firm (management,
products, or operating procedures).
d. Reaction to efforts by the corporation to sell
e. Determinations made by other competent
authority (courts or regulatory agencies).
f. Opinions of expert witnesses.
g. Catastrophic events (destruction of assets,
loss of key personnel, or nationalization).
9. Corporate Reorganization. 10. Receipt of Distributions After Claimed Year of
Selection of Variables for Analysis
Ten general categories of variables were identified in
answering Research Question 1. When these variables were expanded to include the variables listed under general variables 7 and 8, a total of twenty-eight variables resulted. Since loss recognition for worthless securities
depends not only upon the fact that the security is worthless at the end of the claimed year of loss, but also upon the fact that it became worthless during the claimed year of loss, it is necessary that a temporal dimension be added to each of these variables to include this aspect of the courts' decision-making process. By expanding each variable to include a "prior," "during," and "after" temporal dimension, a total of eighty-four variables resulted.
Since the research techniques used to identify these
factors looked at specific cases and references to speciii(3
cases, it was possible that some of these variables woul,] only be found in a small number of cases. To avoid analyzing variables having little relationship to a substantial number of cases included in this study, only
those variables occurring in ten percent or more of all cases are analyzed. These variables and their respective
occurrence rates in each trial court are shown in Table 3.1. The operational definitions used to identify these variables and discussion of how they have been used in court decisions are presented in the pages that follow.
VARIABLE OCCURRENCE RATES
Tax Court District Court
Variable* Decisions Decisions
1P-Insolvency 25% 20%
lY-Insolvency 36 32
2P-Receivership 19 12
2Y-Receivership 4** 10
4P-Foreclosure 8** 12
5BP-Actual Liquidation 11 17
5BY-Actual Liquidation 33 29
6P-Operating Losses 31 29
6Y-Operating Losses 25 27
Business Activity 20 22
Business Activity 23 32
7BP-Market for Firm's
Principal Products 10 2**
7BY-Market for Firm's
Principal Products 10 5**
7FY-Proceeds from Sales
of Stock 6** 10
Future Profitability 17 12
8AY-Market for Firm's Stock 6** 12
*P = Occurrence prior to claimed year of loss. Y = Occurrence during claimed year of loss.
**Occurrence rate does not exceed ten percent cutoff, but is
presented for comparison purposes.
Operational Definitions of Variables
Insolvency is included as a variable when (a) it is specifically mentioned in the court opinion or (b) when insolvency is not specifically mentioned by the court but financial statements contained in the opinion indicate total liabilities exceed total assets. indicating the importance
oE insolvency, the Tax Court stated in its decision in the Kleberg case regarding whether or not stock held by the taxpayer was worthless in 1934
The record here reveals that the company was, in
reality, insolvent at the close of 1934 and that its stock then had no actual or potential value.
We cannot disregard realities. The stock became
worthless in 1934.7
The values used by the courts to determine insolvency are market values, if such values are in fact available In the event market values are not available, the courts will consider book values.9 While insolvency may indicate lack of current value, it does not necessarily indicate
worthlessness since it does not establish lack of potential future value. This point was discussed by the court in Olds & Whipple v. Commissioner, which stated
The fact that the assets were insufficient to meet tile operating liabilities may properly be taken as
evidence of worthlessness of stock, but it is not
conclusive. Actual worthlessness should be the
test, and if those in charge of the operations of
the corporation, acting in good faith, believe
that they might work out ol i-,-ieir business
conditions wherein losses were sustained, and did
so, realizing some profit and reducing the
deficit, it may not be said that the stock was
actually worthless. A real loss is sustained when
all changes or possibi-litiei 0 of collection have
been effectively destroyed.
Receivership is a factor when the court's opinion makes specific reference to (a) receivership, (b) the appointment of a trustee at the direction of another court, or
(c) acceptance of a trustee by either shareholders, creditors, or a creditors' committee. In Melick, the Board of Tax Appeals found that the shareholder's stock in a bank, that became insolvent and was placed in receivership during 1921, but which continued to operate until 1923, became worthless during 1921.11 Even though operations continued, the court found that no profit was being generated and the
bank was only concluding prior transactions. Such actions indicated no possibility of recovery from the loss of value incurred by the shareholders during 1921.12 Similarly, -in Schoenhut, the Board of Tax Appeals found that shares of stock in a corporation that became insolvent and was placed in receivership during 1935, but did not have its assets sold by the receiver until 1937, became worthless during 1935.13 The critical factor in the Board's decision was that 'che proceeds of the sale in 1937 were not expected to,
and did not result in, realization of any proceeds for the shareholders. However, in Lawson, the Board of Tax Appeals also held that shares of stock in a corporation that was
placed in receivership during 1932, but reorganized in 1936 with the shareholders of the original corporation receiving equity in the new corporation, were not worthless.14 These
cases indicate receivership will probably be regarded as an event demonstrating the loss of both current and future value if the shareholders do not realize any return on their
shares in a subsequent taxable year.
Foreclosure is considered a factor when the court's
opinion (a) specifically mentions foreclosure or (b) refers to creditor suits seeking possession of principal corporate assets. In Ladew, the Board of Tax Appeals indicated the significance of foreclosure in determining whether of not worthlessness had occurred.'5 In part, its discussion provided
In support of the contention of worthlessness the
returns of the corporation were put in evidence, with reliance mainly upon the balance sheets as
reported in the returns, reflecting before
financial reorganization an enormous operating
deficit. The corporation, however, was able to
hold of f its creditors until some time in 1926; it
had behind it the earnest support and backing of
the petitioner; and its troubles were largely due
to general adverse trade conditions, so that we
think it can not be said that prospects were
hopeless for a financial rehabilitation.
The regulations of the Commissionerf have
uniformly required that a loss through worthless
stock is only allowable through a closed
transaction or where there Is a clear showing
that the stock is utterly without any value
However bad the statement of affairs appears
from the balance sheet at the beginning of 1923,
it is not a basis upon which we think the
respondent, in the face of continued operations,
would have permitted the petitioner to have taken,
in a prior year, the deduction of loss through
In 1926 the creditors closed down on
the corporation and liquidation immediately
began . there remains a heavy loss, for we see
no chance whatever for the petitioner to realize
anything on the remainder of his no-par co-mmon stock, and we believe there is a satisfactory basis for a conclusion th this no-par stock
became worthless in 1926."
Also indicating the relationship of foreclosure to the
determination of worthlessness is the decision of the
Second Circuit Court of Appeals in Friend.'7 In
deciding whether the Board of Tax Appeals was correct in its
conclusion that the taxpayer's stock became worthless in
1931 (instead of 1932), as claimed by the taxpayer, this
Now, in our case, counsel for the petitioners
insists that the Board failed to give effect to the value attributable to the stock by reason of
the right of redemption. It will be enough to say
that the worthlessness of a share of stock as of a particular year is a question of fact, requiring a
practical consideration of all the facts and
circumstances, .. and that proof of worthlessness of stock of an insolvent corporation
is not dependent upon the com-rpletion of
liquidation proceedings where the facts clearly
indicate a total loss occurred prior thereto. ...
To be sure, foreclosure and sale of the property
did not of itself necessarily establish the
worthlessness of the stock, but it is a factor to
be considered along with the other facts and
circumstances in determining whether the stock was
worthless in 1931.
The record in this case discloses that the
Sheridan Grace Corporation was organized for the
specific purpose of building and operating an
apartment building which was completed too late to
obtain satisfactorcy r -sults for the rental season
of 1929; that during the first 14 months of
operation the gross income was about $200,000,
only slightly in excess of the interest charges on
the first mortgage bonds; that only two payments
of interest were inade on the first mortgage bonds,
no payment of the second mortgage bonds being
oiaie, and that at the time of the foreclosure sale
there were also other judgments and creditor's
claims in excess of $50,000.
The Board, after weighing and considering all
the evidence presented, found that the evidence
did not show that the corporation's equity of
redemption had any fair value at any time, or that
the shares of stock could have been sold for
anything after October 8, 1931, and found as a
fact that the corporation was hopelessly insolvent
in 1931 and that the loss was sustained in that
Under these circumstances we cannot say that
there is not substantial evidence to support the
These cases indicate that foreclosure is not sufficient to
establish worthlessness unless it is also accompanied by
other evidence indicating no remaining value for the
This variable was included whenever liquidation or
dissolution was discussed in the court's opinion.
Liquidation following foreclosure was regarded as sufficient
evidence by the Board of Tax Appeals to establish
worthlessness in Ladew.19 However, as the Second Circuit
Court of Appeals held in Friend, liquidation does not always
establish worthlessness.20 In Conover, taxpayers tried to
use corporate 3is-3olution in 1941 to establish worthlessness
of stock in a corporation that had most of its assets taken
over by creditors in 1937.21 The Tax Court's opinion
The burden was therefore upon the petitioners to show that at the end of 1940 the Brookmont stock
had value, for the actual dissolution of the
corporation in 1941 could not indicate loss of
value if none then remained. After careful
examination of all of the facts here presented to
us, we are forced to the conclusion that the
petitioners have not inet the burden imposed upon them. It is not without reluctance that we deny
deduction for loss in the year when there is final corporate dissolution; yet the circtios nces here
leave, in our opinion, no alternative.
Also, it is not necessary for liquidation to occur in
order for worthlessness to be established. In Jackling, the
IRS took this position in an attempt to deny a taxpayer's
claim that stock he held through a partnership interest
became worthless during 1918 when the corporation aband,,oned
its lumber operations.23 In deciding this issue, the Board
of Tax Appeals stated
We are of opinion that the partnership, the
Pacific Rice Mills, sustained a loss in the fiscal
year ended October 31, 1918, in the amount
claimed. The evidence shows that it invested in
the stock of the corporation the amount of
$25,000, and that it advanced the corporation money to continue its business until February
1918, when having determined that the operation of
the corporation would always be unprofitable, it
caused the corporation to cease its activities and
advanced further funds to liquidate the
corporation's indebtedness. The advances after
February 1918 were made because under the laws of
California the partnership, as sole stockholder of
the corporation, was liable for its debts. The corporation had no assets other than the timber
lease, which under the circumstances was in
reality only a continuing liability. The fact
that the corporation was not dissolved does not,
in our opinion, affect the question presented
The implication of these cases is that liquidation, similar
to foreclosure, does not establish worthlessness unless
accompanied by other events that indicate a total loss of
This variable was included if the court's opinion (a)
referred to operating losses, (b) discussed operating
deficits, (c) mentioned unsuccessful efforts or operations,
or (d) contained financial statements showing losses.
Courts have not found this variable sufficient to
establish worthlessness. This point was made by the Board
of Tax Appeals in the following discussion from its decision
in Burden when it stated that
In this proceeding the evidence establishes that,
while the Products Corporation was experiencing
some financial difficulties during 1933, the
extent of which is not fully disclosed, it was a
going concern which had sales in excess of
$16,000,000 during that year and had assets in
excess of $25,000,000 at the close of 1933, valued on a going concern basis. There is no evidence of
insolvency of the Products Corporation during 1933
even though it did sustain an operating loss of
approximately $602,000 during that year and
experienced difficulty in the collection of the
subscriptions made under the 1932 plan of
reorganization of the Operators Co. During 1933
the Products Corporation collected approximately
$180,000 of such subscription and there is no
evidence of what portion, if any, of the unpaid
subscription, amounting to approximately $719,000,
carried as an asset at the end of 1933, was
definitely uncollectible. The fact that there had
been a shrinkage in the value of the Products
Corporation common stock owned by C.C. Burden and
that the conditions existing at the end of 1933
may have been such as to lead him to his
conclusion that, without a change for the better,
he probably would sustain a loss on his investment
in such stock, is not sufficient to establish
actual worthlessness in that year.25
While operating losses do not establish worthlessness
in the claimed year of loss, the courts have examined
operating losses in determining whether the stock in
question became worthless in a prior year. In Olds &
Whipple v. Commissioner, the Second Circuit Court of Appeals
found that operating losses accompanied by earnest
expectations of the taxpayers that economic conditions would
improve did not establish worthlessness prior to the claimed
year of loss.26 However, in William C. Squier v.
Commissioner, the Second Circuit Court of Appeals
reached the following conclusion for stock of a corporation
that experienced significant operating losses and operated
only through advances of capital from the taxpayer
We are satisfied that the stock of such a
hopelessly insolvent corporation as Shur-Loc Elevator Safety Company, Inc., was worthless
during the taxable period. But so far as we can
see it was worthless some years before. The
record shows an operating loss from the
organization of the Shur-Loc Elevator Safety
Company, Inc., in 1914 up to November 30, 1926 when it ceased to do business. Prior to January 1, 1926,
the loss had already aggregated $322,765.82. The
burden was upon the executors to establish that
the stock, the cost of which they seek to deduct,
became worthless during the taxable year. But it seems quite evident that it was equally worthless
the year befor 7 and doubtless for several years
prior to that.
These cases indicate that continuing operating losses,
without evidence that they are expected to be eliminated,
may provide the courts with a basis to f ind that stock became worthless prior to cessation of business activities.
Discontinuation of Business Activities
This variable was included whenever the court's opinion mentioned that a firm's principal line of business was discontinued. The importance attached to this factor by the courts seems to vary with the context of its occurrence. In
Jacklinq, the Board of Tax Appeals found stock in a corporation that abandoned its lumber operations in 1918, but did not formally liquidate, became worthless in the year its operations ceased.28 However, in Rand, the Board of Tax Appeals found the stock of a corporation that had continued its operations through 1934 to have become worthless prior to 1934.29 In reaching this conclusion the court stated
Petitioner urges that at all times the
Reorganization Investment Co. continued in the
operation of its business and was at all times
able to pay its current obligations as they
matured. The continued operation of the company
does not of itself prove value in its stock. . .
Moreover, the company by its very nature was a
liquidating company, and would presumably continue
to operate until its purpose was fulfilled, even though the final result of its operations could
leave nothing for stockholders.To
These decisions indicate that information, in addition to this variable, is used by the courts in reaching decisions regarding worthlessness.
Market for Firm's Principal Products
This variable was included when the court's opinion
discussed the absence of a market for the corporation's
primary products. The Board of Tax Appeals in Corbett
expressed its regard for this variable in reaching the
f ol lowing conclusion
In 1923 petitioner sold for $10 corporate stock
for which he had paid its par value, $18,000, and
in 1925 he again sold for $10 stock in the same corporation for which he had paid par, $27,500.
The respondent concedes that a deductible loss was
sustained by the sale in 1923, but contends that in that year the petitioner determined the stock to be worthless and therefore no loss should be
allowed in respect of the sale in 1925.
That conclusion is not justified by the
evidence. Although conditions affecting the sheep
and wool industries were not good, many of the
Basin Wool Co.'s borrowers had shown improvement.
The market price of wool had more than doubled and
the outlook for the company in 1923 was by no
means hopeless. The large loan to R.W. Stanfield gave promise as late as July 1924 of working out successfully. Not until the fall of 1925 was it
known that the loan could not be collected.
Petitioner testified that in 1923 he did not know
the value of the Basin Wool Co.'s stock and that his sale of the stock in that year was purely for
the purpose of taking an income tax loss. The
fact that he sold the stock for a nominal sum,
under the circumstances set forth, does not prove
that petitioner had det ruined the stock to be
worthless at the time.3?
The Board of Tax Appeals in its Pearsall decision
also cited market conditions along with other factors, in
reaching a conclusion regarding whether stock of the
taxpayer became worthless in 1921 when operations ceased or,
as claimed by the IRS, during 1922 when the corporation went
into receivership.32 The court stated
From the foregoing statement of facts it is
apparent that the Railway Specialty Co. was
insolvent in 1921. At that time it had a deficit
of $50,000, with an uncollectible account
receivable of about $60,000; it was unable to sell its manufactured product; it could not pay overdue interest on borrowed capital; and its stockholders
apparently did not have sufficient confidence in
its ability to recover to invest additional money
in the enterprise. Additional evidence of the
worthlessness of the stock is found in the
unsuccessful attempt made by the petitioner to find a purchaser for his holdings at any price.
Developments subsequent to 1921 confirmed the
The stock was worthless at the close of 1921
and the cost thereof was a deductible loss
occurring in that year.33
From these cases it appears that courts regard
marketability of the firm's principal products as an indicator of potential future value for the corporation's stock.
Proceeds from Sales of Stock
This variable was included if the taxpayer had sold any of the stock in question and this sale was contained in the court's opinion. The courts' regard for this variable is mixed. A prime example is the Board of Tax Appeals action in Corbett.34 Sale of stock for a nominal amount in 1923 was not regarded as a sufficient basis to establish worthlessness in that year; however, a sale of the same stock for a nominal amount in 1925 was associated with worthlessness. The reason for this inconsistent association
of nominal selling price with worthlessness is apparently due to other factors the court considered more relevant in
determining worthlessness. In this case, the 1923 sale was associated with a firm that was facing improving business
conditions, where the 1925 sale was associated with the same firm having no future expectations of recovery.35 This
seems to indicate that while the courts may discuss the sales price of a firm's stock, other variables will be given more weight in determining whether or not the stock is worthless.
Opinions Regarding Future Profitability
This variable was included if the taxpayer or
corporate management's opinion regarding the prospects for the future profitability of the firm was contained in the
court's opinion. In Olds & Whipple v. Commissioner, the Second Circuit Court of Appeals held that a corporation's stock was not worthless, even though the corporation was insolvent, because the taxpayers continued to operate the corporation under the belief that conditions would
improve.36 Similarly, in Olson, the Tax Court placed a great deal of emphasis on this variable.37 In this case the
following facts and opinion were presented in the court's opinion
In 1935 petitioner with two others incorporated
the Trask-Willamette Co. for the purpose of
logging timber partially damaged by fire in a
tract in Oregon. . The other assets of the
corporation consisted of the timber contract
permitting the logging of the territory. This
contract covered approximately a billion feet of
fir timber at a very advantageous price to the
corporation. The early operations of the corporation, however, resulted in a substantial operating deficit prior to 1939. In that year a second fire attacked the lumber tract and
destroyed a number of railroad bridges on the only railroad supplying transportation to this tract.
In this fire much of the corporation's mortgaged equipment was destroyed. In September 1940 the bank brought foreclosure proceedings, and after the purchase of the equipment by the mortgagee at the foreclosure sale there was a deficiency of approximately $24,000. . The resumption of this logging operation would have required
additional capital to procure this equipment and either a rebuilding of the railroad or the procurement of trucks and a roadway for the shipment of logs.
At the end of 1940 the only asset retained by Trask-Willamette was the timber contract. During 1941 all prospects of repairing the railroad vanished, the railway equipment was sold, the
receiver discharged, and Trask-Willamette rejected the idea of constructing a road to remove the logs by truck. In March of 1941 petitioner disposed of his stock in the corporation to one of his associates in the enterprise for a nominal consideration of $1. He claimed a capital loss in 1941 . .
The petitioner testified that even after the
1939 f ire and the sale of the equipment in 1940 he still thought the lumbering rights of TraskWillamette were of such a profitable character that he considered the possibility of constructing
a road into the site and removing the lumber by truck. The receiver of the railway company
meantime was energetically endeavoring to refinance the railroad. He did not give up his efforts and file his final report until August of 1941.
All of the evidence shows that the petitioner was an outstanding man in the lumber business, whose judgment was considered sound by leaders in that f ield. . Should we join with the Commissioner in a hindsight view, it does seem
that after the equipment foreclosure sale in 1940 there was not much value left in Trask-Willamette stock. However, due to the advance of war prices in lumber and the advantageous price which TraskWillamette had on stumpage, our hindsight now tells us that, if petitioner and his associates
had persisted into the war years, Trask-Willamette
would doubtless have been really profitable. In 1940 and 1941 all such questions were conjectures into the future and we would be most reluctant to
say that the petitioner was not 4gstified in
taking his capital loss in 1941.
These cases show that the courts place considerable
emphasis on the beliefs of taxpayers regarding future
profitability. Fact situations, which in other cases, have
been used as a basis for establish worthlessness, were not
found sufficient to establish worthlessness when this
variable is present.
Marketability of the Corporation's Stock
If the court's opinion discussed the selling price of
corporate stock by any party other than the taxpayer, this
variable was included. In George H. Hornin2 a market for
the firm's stock was mentioned in the Board of Tax Appeals
opinion deciding if the taxpayer's stock became worthless
during 1932 when receivers were appointed for the
Worthlessness of petitioners' stock was not
established in 1932 merely because receivers of
the Utilities Co. were appointed by a court. The
report of the valuation auditor mentioned above
shows that as late as 1934 stock of the Utilities
Co. was listed on the New York Curb and both its
preferred and common stock were then traded in.
The stipulation by the parties in this proceeding
shows that in 1932 stock quotations on the
character of stock owned by t1lese petitioners and
here involved indicate that both preferred and
common had value--were not absolutely or
practically worthless--and were in 1933 also
quoted at a lower figure.
It is true that the plan of reorganization
dated September 24, 1934, embodied the statement relied on by petitioners, that the preferred and
common stockholders of the Utilities Co. had no
equity in its assets, its liabilities to its
creditors being in excess of $65,000,000. That
situation or condition did not, however, appear to
exist in 1932, when the noteholders' committee
reported it found much "in the present to suggest
an optimistic view of the future."
After carefully considering the entire
record, we find no identifiable event which
establishes thg9worthlessness of petitioners'
stock in 1932.
However, in John B. Marsh, the Tax Court found quoted market
prices were not sufficient to establish that the stock in
question was not worthless in the claimed year of loss.40
The court provided the following discussion of this finding
The respondent contends that the "over the
counter" sales of the preference stock, made
within the price ranges per share of a high of 062
cents and a low of 12 1/2 cents in 1932, f ol lowing the month of May, of a high of 25 cents and a low
of 17 1/2 cents, in 1933; of a high of 16 1/2
cents and a low of 10 1/2 cents, in 1934; and of a high of 27 1/2 cents and a low of 11 1/2 cents in
1935, established that the stock continued to have
value, not only throughout 1932 but during
subsequent years through 1935. Applying the
foregoing per share prices to 750 shares of
preference stock, the number of shares owned by
Isabel S. Marsh, and making allowance for
brokerage commission and transfer taxes, the
respondent computes maximum and minimum values for
the block of stock as follows: $429 and $54 in 1932; $135.75 and $79.50 in 1933; $72 and $27 in 1934; $154.50 and $34.50 in 1935. The recor(I is
silent as to the number, frequency, or size of the
sales upon which the respondent relies. Whether
they were scattered, isolated transactions
involving only a few shares each, we do not know.
Aside from the showing that they were made "over
the counter," nothing is revealed of the
circumstances surrounding any of them. In view of
this condition of the record and of the public sales made about the end of 1932, the proceeds
from which did not rneet the expenses thereof, and
considering the generally recognized insolvent
condition of International in 1932, we think that
these sales upon which the respondent relies, were
of a type that is made for the purpose of
establishing losses or represent purchases made by
optimists in defiance of reason and the generally
known and accepted facts. Transactions of that
type do not establ h value for stock that is
These findings seem to indicate that the courts will only
regard a market for the corporation's stock as a factor not
indicating worthlessness if the price quoted for the stock
is high enough to cover the selling costs of investors
holding the stock.
lCommerce Clearing House, Inc., Standard Federal Tax Reports (Chicago: Commerce Clearing House, Inc., 1984).
2Callaghan & Co., Mertens Law of Federal Income Taxation (Wilmette, Ill.: Callaghan & Co., 1984).
3Prentice Hall, Inc., Federal Taxes (Englewood Cliffs, N.J.: Prentice Hall, Inc., 1984).
4Research Institute of America, Inc., Federal Tax
Coordinator 2d (New York: Research Institute of America, Inc., 1984).
5Tax Management, Inc., Tax Management Portfolio No. 96 3rd [Losses-General Requirements] (Washington, D.C.: Tax Management, Inc., 1984).
6J.g. Worthy, "Stock Losses: Establishing
Worthlessness," in Proceedings of New York University Twenty-Second Annual Institute on Federal Taxation (New York: Matthew Bender & Co., Inc., 1964).
7Alice G.K. Kleberg, 2 TC 1024 (1943).
8Blanchard S. Forbes v. Commissioner, 62 F.2d 571 (CA-4, 1933).
9B.F. Edwards, 39 BTA 735 (1939).
1001ds & Whipple v. Commissioner, 75 F.2d 272 (CA-2, 1935).
11J.J. Melick, 6 BTA 70 (1927).
13George W. Schoenhut, 45 BTA 812 (1941).
14Edward C. Lawson, 42 BTA 1103 (1940).
15J. Harvey Ladew, 22 BTA 443 (1931).
17Milton H. Friend v. Commissioner, 119 F.2d 969 (CA-7, 1941).
19J. Harvey Ladew, 22 BTA 433 (1931).
20Milton H. Friend v. Commissioner, 119 F.2d 969 (CA-7, 1941).
21Henry S. Conover, 4 TCM 367 (1945).
23D.C. Jackling, 9 BTA 312 (1927).
25John W. Burdan, 37 BTA 642 (1938).
2601ds & Whipple v. Commissioner, 75 F.2d 272 (CA-2, 1935).
27William C. Squier v. Commissioner, 68 F.2d 25 (CA-2, 1933).
28D.C. Jackling, 9 BTA 312 (1927).
29Frank C. Rand, 40 BTA 233 (1940).
31Elliott R. Corbett, 28 BTA 46 (1933).
32Gilbert H. Pearsall, 10 BTA 467 (1928).
34E11iott R. Corbett, 28 BTA 46 (1933).
3601ds & Whipple v. Commissioner, 75 F.2d 272 (CA-2,
37E.C. Olson, 10 TC 458 (1928).
39George H. Horning, 35 BTA 897 (1937).
40John B. Marsh, 38 BTA 878 (1938).
This chapter primarily discusses the design used to answer Research Questions 2-5. Prior to this discussion, the general methods of analysis are identified and the
coding of decisions discussed. Additionally, limitations in the research design are identified.
Method of Analysis
Because of the large number of cases identified for
study in this dissertation, traditional legal research may be an impractical method of determining how the variables identified in these cases relate to the decisions of the courts. In addition to possible limitations of human
information processing in deriving a relationship among the identified variables for a large set of cases, traditional
legal research may be affected by interjection, whether or not intentional, of the researcher's personal biases. This research seeks to avoid both possible limitations by using a more quantitative approach that relies on mathematical and statistical analysis performed with the aid of a computer.
To assess the validity of this assumption that
quantitative analysis is superior to traditional legal research when a large number of cases are present, an
heuristic model will be developed for comparison purposes in Research Question 3. This assumption would appear justifiable if the classification accuracy of the quantitative model is superior to that of the heuristic model.
Two methods of coding the previously identified
variables were considered. First, each variable could be represented in terms of three values. For example, insolvency (Variable 1) could be coded as follows: (a) if insolvency was mentioned in favor a finding that a particular stock was worthless, this could be represented by
1; (b) if the corporation was not insolvent and the court mentioned this, -1 would be used; and (c) if solvency or insolvency was not mentioned, this variable would be represented by 0. This model would be expressed as
Y = Bo + BlXl + e,
Y = the probability of a stock being found worthless,
X = the independent variable,
B = the independent variable coefficient, and
e = the error term.
The expected values for this model are
E(Y X1 = 1) = Bo + Bi
E(Y Xl = -1) = BO Bl, and
E(Y X1 = 0) = BO.
Second, an alternative approach could be used where
each variable could be represented by two dummy variables. Again, using variable 1, insolvency, the following coding scheme would result: (1) if the corporation was insolvent and this fact was discussed by the court, variable X, would be coded as a 1 and otherwise a 0 value would be assigned;
(2) if the corporation was not insolvent and this fact was discussed by the court, variable X2 would be coded as a 1 and otherwise a 0 value would be assigned; and (3) if insolvency or solvency were not mentioned by the court, both variables Xl and X2 would be coded as 0.
This model would be expressed as
Y = BO + BlXl + B2X2 + e
and would have the following expected values
E (Y X, = 11 X2 = 0) = Bo + B,
E(Y X1 = 01 X2 = 1) = BO + B2, and
E (Y Xl = 0, X2 = 0) = BOThe difference between these two coding methods is not readily apparent until a comparison is made between the values each model assigns to a variable when it is mentioned by the court in worthless and not worthless decisions.
Model 1 assigns the same value (Bl) to a single variable (insolvency) in both worthless and not worthless decisions. In contrast, Model 2 assigns unique values (Bl and B2) to single variables in worthless and not worthless decisions. This distinction means that Model 2 may utilize more of the information contained in the data than does Model 1. Model
2 does, however, have a limitation in that it doubles the number of variables required for analysis thereby increasing the complexity of the analysis and possibly reducing the statistical significance of findings related to a small population.
The relative benefits of using this coding technique
may not be significant. Stewart found that the use of Model
2 only increased the ability to discriminate between employee and independent contractor status by 1.3 percent For purposes of this research, both coding schemes will be
used to determine the difference, if any, that the choice between alternative coding techniques may have on the results of this study.
Coding Individual Cases
Each case was examined and the identified variables
were coded when they satisfied the operational definitions
developed in Research Question 1. Copeland, Taylor, and Brown have noted that observation error in variable coding may adversely affect findings in tax research To minimize the potential effects of this type of error, operational definitions were provided for each variable prior to coding which used discrete versus continuous values. To determine the potential magnitude of observer error included in the coding of cases for this study, a sample of approximately 10
percent of all cases (40) were independently coded and compared with the original coding. The results of analyzing the comparative coding indicated that 5 of the 3360
identified variables had originally been coded incorrectly. These errors affected different variables providing a basis to conclude that a search for systematic errors in the
entire population would likely not produce any significant results. The identified coding errors were corrected but additional possible coding errors were not searched for
since the error rate in this sample was less than 1 percent. If this sample is representative of the population, the
inclusion of any remaining errors should have an insignificant impact on the results of this study. Support
for this assumption can be found in a study by Pollard and Copeland who found that the accuracy of discriminant model
predicting the outcome of "tax home" cases was reduced by 2 percent when a 3 percent random coding was introduced into the data used to construct their model.3 The sensitivity of
the models developed in this study, with respect to the introduction of random coding errors will be tested in Research Question 6.
In coding the selected decisions from the Federal
district courts and the Tax Court, it was discovered that 20 (5.7%) of the Tax Court cases did not contain any of the variables selected for analysis. These 20 decisions were reviewed to determine whether their elimination from the study would result in a significant loss of data. The only unique feature discovered in the analysis of these cases was a consistent relationship between the presence of Variable 9 (Corporate Reorganization) and the findings of the court in five of the cases. In four decisions where the shareholders received nothing for their prior equity interests, the court found their stock worthless. In a fifth decision where the shareholder received an equity interest in the reorganized corporation, the court found the stock not worthless. These findings imply that while reorganizations may not be a frequent event, what shareholders receive (or do not
receive) in the reorganized corporation has a consistent relationship to the decisions of the court. In the remaining fifteen decisions no consistent relationship between court decisions and specific variables was discovered.
Research Question 2
Court decisions regarding worthlessness may result in only one of two possible outcomes: either the stock is
worthless or the stock is not worthless. Since these decisions are strictly binary, it is not possible for the court to find a stock anything less than 100 percent worthless. This binary characteristic makes analysis using mathematical models that allow dependent variables to be
represented by a continuous range of values (e.g., multiple regression) inappropriate. Multiple Discriminant Analysis (MDA), however, is appropriate for analyzing the relationship between a series of independent variables and a binary dependent variable. This technique searches for two
classification functions relating to the binary dependent variable, that will linearly combine the independent variables to give a probability of membership in each group
(worthless or not worthless in this study) for each observation. Individual observations will be assigned to
the group having the classification function which creates the highest probability of membership score when applied to that observation.
The SPSS-X Discriminant computer software program will be used to derive a discriminant function for those variables occurring in 10 percent or more of the cases
selected for analysis.4 The model developed by this program is of the general form
D =diXi+ d2X2 + +dnXn
D = the score of the discriminant function,
X= the n discriminating variables selected for
d= the weights for each X variable.
From this discriminant function, classification functions can be derived that will indicate the probability of a particular case belonging to either of these two categories. The classification function for each group could be written as
C= Cl1+ + . + + CpVp + Ki
C= the classification score of the ith group,
C = the classification coefficients,
Ki = the constant, and
Vi = the observations from the individual cases.
This function may be used to calculate a classification score for each decision for both groups (worthless versus
not worthless). A decision will be assigned to the group for which it has the highest classification score. Finally, it is possible to convert the classification scores to probabilities of group membership. The classification of a case into a particular group is, in fact, the same as attributing the decision to the group for which it has the greatest probability of membership.5
If classification functions are used to predict the
group membership of the same cases that were used to develop
the classification functions themselves, an upward bias in the classification accuracy of the model may occur. Two procedures will be used to help overcome this potential bias.
First, for the 328 Tax Court decisions, the Statistical
Analysis System (SAS) computer program DISCRIM will be used to derive a discriminant function for the selected variables from approximately one-half of the decisions that will be selected at random.6 This discriminant function will then
be used to classify a holdout sample of remaining decisions. The selection of the holdout sample will be accomplished by assigning a normally distributed random variable having a range of 0 to 1 to each decision. If the value of the
variable is less than .5, the casewill be assigned to the
group used to develop the discriminant function. Otherwise, the case will be assigned to the holdout sample. Second, the classification accuracy of the model developed for Federal district court decisions will be examined using a different technique. Since there are only 59 decisions,
statistically meaningful results may not be obtained by using the holdout sample method as was possible with the 328 Tax Court decisions. An alternate validation procedure from
the P7M computer program of the Biomedical Computer Program P Series (BMDP) that is more statistically appropriate will be used instead.7 This technique is known as the "jackknife validation procedure" that was initially proposed by Lachenbruch.8 This procedure involves calculating a discriminant function based on all but one decision. This discriminant function is then used to develop classification functions to classify the omitted decision as worthless or not worthless. This technique is then repeated leaving out a different decision each time until all decisions have been classified. To determine how well this technique compares
to the use of a holdout sample, it wi 11 also be used on the 328 Tax Court decisions and the respective results will be examined.
Statistical Considerations of MDA
The use of MDA is based on statistical assumptions that
the independent variables have a multivariate normal distribution, the dispersion matrices within each group are
identical, and that the selected variables contain the actual parameters used by judges in reaching their decisions.
Since the coding scheme used in this research assigns only one of three values to each independent variable, the first condition is violated. Two studies have indicated
that a linear discriminant function is sufficiently robust to perform well in spite of violating the multivariate normal assumption.9
To determine whether the equal dispersion assumption is satisfied, the SAS DISCRIM Procedure POOL = TEST option will be used. If the within group covariance matrices are equal,
a pooled covariance matrix will be used.
When the equal dispersion assumption is violated, the use of a quadratic estimation procedure is considered appropriate.10 Even though the quadratic estimation technique is theoretically preferred when within group covariance matrices differ, Gilbert has demonstrated that use of a linear model produces similar results.11 In some cases, Gilbert even found the linear method superior to the quadratic. Because these findings suggest that results obtained by using either method may not significantly
differ, only linear classification functions will be used since the SAS DISCRIM and SPSS-X Discriminant programs have no options for quadratic functions.
Eisenbeis has made the following observation regarding the use of pooled versus individual covariance matrices to construct a linear model from a small but fixed sample
When the dispersions are similar, this leads to relatively more efficient linear classification results which are not swamped by the effects of
averaging the group dispersions. However as the
differences in the dispersion increase, the
efficiency of the linear parameter estimates begin
to become dominated by the effects of the unequal
Since Eisenbeis does not specify how a large sample may
be distinguished from a small sample, it is possible that matrix choice may affect the findings of this research. To test for this potential effect, the accuracy of classification functions based on a linear discriminant
function derived from individual versus pooled covariance matrices will be compared.
A discriminant function that is solely based on an
analysis of the relationship between individual and dependent variables may fail to accurately classify observations unless additional parameters are considered.
Lachenbruch specifically recommends the consideration of the cost of misclassifying observations and the a priori probability of group membership.13
Consideration of group misc lass if ication costs is
relevant only when the costs of misclassifying observations between groups are significantly different. Since Tax Court
decisions are subject to possible review by an appellate court, it is assumed that judges consider the possibility that their findings may be reversed as the only cost of
misclassification. If judges only regard misclassification costs in terms of accuracy, it is not necessary to include
this parameter in the discriminant function that will be developed since these costs are equal.
Eisenbeis has found that misclassification rates
increase when differences in a priori probabilities of group
membership are not considered.14 Even though prior probabilities for the decisions examined in this study are
approximately proportional (.49 worthless and .51 not worthless for Tax Court decisions and .58 worthless and .42 not worthless for Federal district court decisions) the effect of differences will be considered. By entering the respective probabilities of group membership into the prior probability options of the selected computer software packages resulting discriminant functions will be adjusted for differences in prior probabilities.
Correct Functional Form
The use of linear discriminant analysis assumes no
interaction exists among the independent variables. This assumption may not hold if judges regard the presence of a particular variable such a strong indicator of worthlessness
that other variables, also present in that specific case, have little influence on their decision. For example, if a corporation was hopelessly insolvent, it may not matter that bankruptcy had not been declared or that the corporation had not been liquidated for a judge to find the corporation's
stock worthless. If judges allow independent variables to interact in this manner, uniform increases in the importance
a judge places on an independent variable would not be accompanied by uniform increases in the probability of a particular outcome as is assumed in a linear model. Instead, this interaction may be more accurately described by a non-linear, tilted S-shape curve, relationship where an independent variable has its greatest impact on changing the probability of a particular finding at the midpoint of this distribution. Since this distribution is steepest at its midpoint and relatively flat at either tail, changes in the importance associated with an independent variable occurring
near either endpoint would have little effect on the judge's finding.
To determine whether a non-linear model better describes the decision process of the Tax Court, the
classification accuracy of a non-linear model will be compared against the classification accuracy of the linear
discriminant function. The non-linear model will be estimated through a "logit transformation" of the dependent
variables. This technique produces an S-shape distribution within the limit of the (0,1) bounds imposed by the presence of binary dependent variables. Stewart has noted that logit transformation is unique among most common non-linear estimation procedures because of its ability to convert
dichotomous dependent variables into continuous variables with (0,1) bounds. A similar non-linear model, profit
analysis, was considered, but not adopted because it assumes
normal distribution of its explanatory variables, which is not the case in logit analysis.
Logit transformation is based on the cumulative logistic probability function
Pi = F(X1 + e (XB) where
P= the probability a judge will find a stock
worthless, given the knowledge of X;
X = the independent variable(s);
B = the coefficients of the independent
e = the base of the natural logarithms
This equation can be solved in terms of eXB, giving
1 Pi= the probability a judge will find a stock not worthless, given the knowledge of X.
By taking the log of both sides, the equation is expressed in terms of the independent variables and their respective coefficients (XB)
XB =log P
Once the parameters of this model have been estimated, the arithmetic process above may be reversed and applied to individual cases to determine classification accuracy. The
SAS LOGIST program will be used to determine how accurately individual decisions are predicted for both Tax Court and Federal district court cases.15
Research Question 3
Construction of the heuristic model requires a
synthesis of statutory requirements, the "identifiable
event" criteria adopted by the courts, and the variables selected for analysis. Generally, a finding of worthlessness depends on the ability of the identified
variables to indicate that the stock in question lost both current and future value during the claimed year of loss. A single variable indicating either form of value may result in disallowance of the loss deduction.
For this reason, the heuristic model is based on values that may be assigned to the identified variables that may
lead to a not worthless f finding by the courts and the temporal distribution (year of occurrence) of all other variables. If a case contains any one of the identified
variables coded in the manner listed below, the finding will be predicted to be not worthless. Otherwise, a worthless decision will be predicted.
Variable Coded Value Interpretation
Insolvency (Y) -1 Lack of insolvency
in claimed year of
Actual +1 Liquidation prior
Liquidation (P) to claimed year of
Operating Operating profits in
Losses (Y) claimed year of loss
Continuity of -1 Operations continued
Operations (Y) throughout claimed
year of loss
If a decision did not contain any of the variables listed above, the temporal distribution of the variables that were present formed a basis for classifying the stock as either worthless or not worthless. If more variables were attributable to events or conditions occurring either
before or after the claimed year of loss, the stock was predicted to be not worthless. Otherwise a finding of worthless was predicted.
The accuracy of this model will be compared with that
of the "best" model developed in answering Research Question 2. The basis for this comparison will be the classification accuracy of each model.
Research Question 4
Since the cases identified for examination in this research span a 62-year period, it is possible that the decision model used by the courts has changed during this period. If the model has changed, a discriminant function
based on all cases would not be as accurate as functions
based solely on pre- and post-change cases. Because of the relatively small number of decisions from the federal district courts, only the decisions of the Tax Court will be examined for temporal stability. To determine whether a change in the Tax Court model has occurred, a discriminant function from the first one-half of the 328 cases decided during the 62-year time period (pre-1941) will be
calculated. This model will then be used to develop a classification function that will be applied to cases decided after 1940. If the percentage of post-1940 cases that are misclassified by the 62-year classification
function and the pre-1941 classification function are not significantly different, temporal stability of the Courts' decision model may be inferred.
Similarly, the current validity of the Tax Court model will be assessed by using the first 90 percent of all decisions (pre-1968) to classify the most recent 10 percent (post-1967). If the classification accuracy for the most recent 10 percent is not significantly different from that
of the earlier 90 percent current validity of the model may be inferred.
Research Question 5
To determine whether the choice of forum has an effect on classifying a stock as worthless or not worthless,
separate discriminant functions will be developed for all
Tax Court and all federal district court decisions, respectively. These discriminant functions will then be used to classify the decisions from the other court. If the classification accuracy for the decisions decided by the other court does not significantly differ from the classification accuracy for the decisions from the court
that were used to develop the discriminant function, it is possible to infer that decision making is consistent across these two courts.
Research Question 6
The sensitivity of the models to random error will be
assessed by changing the initial coding of the variables and comparing the models based on the modified data with the
models based on the original data. Changes in the coding of variables will be made randomly in the manner suggested by
Pollard and Copeland as follows16
If the original and the random then change the
code is number is original code to
0 0-4 1
0 5-9 -1
1 0-4 -1
1 5-9 0
-1 0-4 0
-1 5-9 1
A 3 percent error rate for Tax Court cases involves changing 118 variables U328 cases x 12 variable) x .03). For the Federal district court cases, 25 variables will be changed U59 cases x 141 variables x .03). The 10 percent error rate required changes to 394 and 83 variables, respectively. The modified data will be used to develop discriminant functions that will be compared with the models developed from the original data. Differences in the weighting of
individual variables or the overall classification accuracy of the models will provide a basis for determining whether the models are sensitive to the introduction of random
A similar analysis will be performed to determine the sensitivity of the models to the introduction of systematic
error. Systematic error will be introduced in the two variables having the greatest contribution to the original models. For the Tax Court model, these variables are 1Y (Insolvency in the Claimed Year of Loss) and 1P (Insolvency Prior to the Claimed Year of Loss). For the Federal
district court model, the variables that will be changed are 1Y (Insolvency in the Claimed Year of Loss) and 5P (Liquidation Prior to Claimed Year of Loss). Systematic
error will be individually introduced by the following transformation of coded values
If the original then the coding
coding is is changed to
The findings of this research may be affected by more
than uncertainty regarding the appropriateness of various statistical and mathematical assumptions that have been made. Several conditions may result in differences between
the factors actually considered by judges and the factors this research has associated with their decisions.
First, in tax litigation the burden of proof is placed on the taxpayer to demonstrate the IRS's position is
inval id.17 For this reason, judges are precluded from considering any relevant information they may be aware of which has not mentioned by the taxpayer. Second, judges'
written opinions may not include all variables presented for consideration since these opinions are not a verbatim record of trial. If a judge includes discussion of enough significant variables to justify his finding to a possible
appellate review, he may not feel that discussing, what he considers insignificant factors, is necessary. Third, it is
possible for individual biases of the researcher to result
in the miscoding of some variables. This limitation should only be minimal based on the low error rate found in the 40
cases that were independently coded.
ID.N. Stewart, Employee or Independent Contractor: An
Examination of the Relevant Variables Employed by the Federal Courts in Deciding the Question (Ph.D. dissertation, University of Florida, 1980).
2R.M. Copeland, R.L. Taylor, and S.H. Brown,
"Observation Error and Bias in Accounting Research," 19(1) Journal of Accounting Research 197 (1981).
3W.B. Pollard and R.M. Copeland, "Evaluating the
Robustness of Multivariate Tax Models: A Section 162(a) (2) Model" (Unpublished manuscript, 1984).
4SPSS, Inc., SPSS-X User's Guide (New York: McGrawHill, 1983).
5N. Nie, Statistical Package for the Social Sciences (New York: McGraw-Hill, 2d ed., 1975).
6SAS Institute, Inc., SAS User's Guide--1979 Edition (Cary, N.C.: SAS Institute, Inc., 1979).
7W. Dixon and M. Brown, BMDP Biomedical Computer
Programs P-Series--1979 (Berkeley: University of California Press, 1981).
8P.A. Lachenbruch, "On Expected Probabilities of
Misclassification in Discriminant Analysis, Necessary Sample Size and a Relation with the Multiple Correlation Coefficient," 24 Biometrics 823 (1968).
9E.S. Gilbert, "On Discrimination Using Qualitative Variables," 63 Journal of the American Statistical Association 1399 (1968); and W.J. Krzanowski, "Discrimination Using Both Binary and Continuous Variables," 70 Journal of the American Statistical Association 782 (1968).
10E.S. Gilbert, "The Effect of Unequal VarianceCovariance Matrices on Fisher's Linear Discriminant Function," 25 Biometrics 505 (1969).
11Id. at 512.
12R.A. Eisenbeis, "Pitfalls in the Application of
Discriminant Analysis in Business, Finance, and Economics," 32 Journal of Finance 879 (1977).
13P.A. Lachenbruch, "Discriminant Analysis," 35 Biometrics 69 (1979).
14R.A. Eisenbeis, supra note 12, at 889.
15SAS Institute, Inc., SAS Supplemental Library User's Guide--1980 Edition (Cary, N.C.: SAS Institute, Inc., 1980).
16W.B. Pollard and R.M. Copeland, supra note 3, p. 7.
17Code Section 7453 and Tax Court Rule of Practice 32.
This chapter contains the empirical results obtained in answering Research Questions 2 through 6. Questions 2 through 4 are separately answered for decisions from the Tax Court and Federal district courts. In the results for Question 5, differences attributable to the court of original jurisdiction are analyzed. Research Question 6
examines the sensitivity of the models developed in this study to the introduction of both random and systematic coding errors. The results of this study are then compared with related research.
Research Question 2
Model construction. In Chapter 111, 12 variables from
Tax Court decisions and 14 variables from Federal district court decisions occurring in 10 percent or more of the respective cases were selected for analysis. As discussed
in Chapter IV discriminant analysis is based on the assumptions that each group is derived from a set of independent variables that possess a multivariate normal distribution and that the covariance matrices for each group
are equal. Since each variable is assigned one of three values in the primary coding technique and only one of two
values in the alternate coding technique, the multivariate normal distribution assumption is violated. Studies by Gilbert and Krzanowski have shown that linear discriminant functions are sufficiently robust to perform well in spite
of violating this assumption.1 To test for equality of the covariance matrices the POOL = TEST option of the SAS DISCRIM program was applied. For the Tax Court model the
Chi-Square value of the test statistic was 224.61 with 78 degrees of freedom which is significant at the 0.0001 level.
The Chi-Square value for the Federal district court model was 181.93 with 105 degrees of freedom which is also significant at the 0.0001 level. These values indicate the group covariance matrices do not satisfy the equality assumption of discriminant analysis. Even though the use of within group covariance matrices is more appropriate, the use of pooled covariance matrices was selected since only the SAS DISCRIM program provides the option to develop a model based on within group covariance matrices and this option only provides the classification accuracy of the model without any coefficients or interpretive statistics. The following section quantifies the difference in classification accuracy between models using a pooled covariance matrix versus within group covariance matrices.
Classification accuracy. Tables 5.1 and 5.2 present
the classification accuracy of models based on within group
WITHIN GROUP COVARIANCE MATRICES MODEL
Actual Group Correct Worthless Not Worthless
Tax Court Model
Worthless 85.5 136 23
Not Worthless 69.8 51 118
Total 77.4 187 151
Federal District Court Model
Worthless 94.1 32 2
Not Worthless 100.0 0 25
Total 96.6 32 27
POOLED COVARIANCE MATRIX MODEL
Actual Group Correct Worthless Not Worthless
Tax Court Model
Worthless 79.2 126 33
Not Worthless 81.7 31 138
Total 80.5 157 171
Federal District Court Model
Worthless 91.2 31 3
Not Worthless 92.0 2 23
Total 91.5 33 26
covariance matrices and pooled covariance matrices. using a
pooled covariance matrix resulted in a 3.1 percent change in the classification accuracy of the Tax Court model and a 5.1 percent change in the classification accuracy of the Federal
district court model. These differences are the result of changes in the cases that were misclassified by each model. For the Tax Court models, 27 decisions that were misclassified by the within group covariance matrices models and 17 decisions that were misclassified by the pooled
covariance matrix model were correctly classified by the other model. For the Federal district court model, 1 decision that was misclassified by the within group covariance matrices model was correctly classified by the pooled covariance matrix model and 4 decisions that were
misclassified by the pooled covariance matrix model were correctly classified by the within group covariance matrices model. The original distribution of posterior probabilities for the 49 decisions that were reclassified is
Group Membership Number Percent
.50-.59 14 28.6
.60-.69 16 30.6
.70-.79 11 22.4
.80-.89 2 8.2
.90-1.00 6 12.2
The above indicates that selecting pooled versus within group covariance matrices models in this study has resulted in a change in the classification for those decisions with a
posterior probability of group membership closest to .5, but has not significantly changed the overall classification of all decisions.
Table 5.3 presents the pooled covariance matrix models for Tax Court and Federal district court decisions showing the standardized discriminant function coefficients, Wilks'
Lambda statistic, and F-Ratio for each variable. The standardized coefficients, when applied to the data also
converted to a standard form, will result in a discriminant score that will have a zero mean and a standard deviation of one. This allows one to interpret the standardized coefficients (when the sign is ignored) as the relative contribution of each variable to the function. This interpretation is analogous to the interpretation of beta
weights in multiple regression.2 The interpretation of Wilks' Lambda and the F-Ratio are inverse. The Wilks' Lambda value indicates the discrimination between groups that is not explained by a particular variable or the entire
model. The F-Ratio indicates the ability of a particular variable to discriminate between the groups.3 Accordingly, a low Wilks' Lambda value and high F-Ratio will be associated with the most significant variables. The overall Wilks' Lambda values are 0.6651 for the Tax Court model and
0.3740 for the Federal district court model.
The variables that are significant at the .05 level and the relative rank of their coefficients in the discriminant
functions for the Tax Court and Federal district court models are
a r- LO 0 a %-D N a OIN a 0 Ln W N LW C 4 0 a w m 110
C; 1 C; C; C C; C; 1 C C;
-4 r wW r-4 0 r--l 1 0 0 M -4 M 0 Ln
41 -W w 0 m .44" r-4 tD Ln 0 0 C14
9 ( C 4 9 1: 4 r : C; C; m CO r--j C14 CN -4 C14
W %D 0 %.D r- r-4 M m
E-4 r-4 0 t.0 -RV M M M W M M 0 0)
z C C; C; C; c; C; C; C C;
m 0 a) 4J 0
N C X 0 m v m M r-4 M r- ko LO r- a
x .14 w r, Ul M N Ln LO r-4 V %D M 0 co
ra 4J %D Ln a m v Ln w m o N LO I",
w 0 Ln N 0 19V N a N m a a
62 E-4 a
co Oct ro 44 0 a C C; C; C; C C C; C; C
4 2: r_ 44
E-4 M W
4J 0 x
W --oo 0)
6.1 w 0 w w w
0 r_ c 04 04
0 0 0
aj .,4.,.4 -j '.4
4J 4J M M r14
M 04 Q
0 a) 00---- ra
(n W w w w >4
04 >I M En rO rO 914 M CO 4J 0-4 -04 0 0 w w 0).,i
-4 0 0 C3 V W 4 W -I
>4 >1 0 0 C: 0 0 w -4
0 u -,-q -4 -4 tw
r- C W 4J -W W W
w a) a) a) (a M -4 -H a C -W 4j 0 41
fu > > > ra ro 41 4.) o o a) 0) .,, -rq
> r-4 --1 -4 -14 -4 co M () u h4 ly a U4
0 0 (1) :3 3 4 W fn M W W -,1 0 W M U 0, Ol a) Q) -4 -- tio m CL w C: r a) 'r-1 Q4 Q4 in M Z Z 0 M 61 0 0 1 1 1 1 1 1 1 1 M >4 aJ >4 >4 >1 >4 m >4 44 m w u
r-4 r-4 (N Ln U) kD D r r- r r r