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"' 99:959‘ 99.9’99 ”999' 9 999 9’99999-9 91999999999 99" 999999 99’ 999999999 9999999 9999.9. 999’ " 9 " "9'" ‘ ‘ " “5W, lIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII STATE 10476 03 mama: EM‘W 88 This is to certify that the dissertation entitled MODELING THE UTILIZATION OF ACCOUNTING DATA: AN EMPIRICAL STUDY presented by David Allen Ziebart has been accepted towards fulfillment of the requirements for Doctor of Philosophy degree in Accounting 5‘25me 0C Ig (\ZF fl9‘\ Major professor £34 Date Afimlq {Mow}?! (IX/i MS U is an Affirmative Action/Equal Opportunity Institution 0— 12771 MSU RETURNING MATERIALS: Place in book drop to .fi? :w nifilfigg ,. r‘ 1.1.; ‘ Ul " LJBRARJES remove this Checkout from w your record. FINES will be charged if book is returned after the date stamped below. fif’f"x*h. Jcfi..0c...25 M ,, Pa, my- 59/3 MODELING THE UTILIZATION OF ACCOUNTING DATA: AN EMPIRICAL STUDY BY David Allen Ziebart A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Accounting 1983 ABSTRACT MODELING THE UTILIZATION OF ACCOUNTING DATA: AN EMPIRICAL STUDY By David Allen Ziebart Previous research evidence indicates that investors react to the issuance of corporate financial information. Earnings data has been found to possess information content. Little evidence on the information usage process regarding other types of financial information is available. A specification of the process by which capital markets use financial data is a necessary prerequisite for understanding the interaction of accounting as an information system and the capital markets as users of the accounting data. This dissertation investigates that process. An investigation of the use of data concerning the liquidity, leverage, profitability, and activity dimensions of a firm by the securities market is conducted utilizing the abnormal performance index research paradigm. Two types of market reaction, abnormal returns and abnormal trading activity, are causally linked to expectation errors regarding the economic dimensions of a firm. Through decomposition of the variation in the market reactions into the components attributable to the variation in the expectation errors of the information cues, the usefulness of each cue is inferred. A causal model configuration is hypothesized, estimated, and tested using Full Information Maximum Likelihood estimation techniques. The results of this study are based upon a sample of two hundred manufacturing firms. These companies are listed on the New York Stock Exchange and possessed the requisite return, trading, and accounting data. The findings of this project indicate that the expectation errors regarding various financial ratios do not fall categorically into the associated liquidity, leverage, profitability, and activity dimensions they are expected to measure. Instead, each ratio must be treated as a unique attribute of the firm. Evidence is found that information regarding the profitability, leverage, and activity dimensions of a firm are used by investors. Market price reactions are found to be linked to the expectation errors regarding the defensive interval and primary earnings per share. Volume reactions are found to be linked to the expectation errors regarding times interest earned, return on total assets, and primary earnings per share. For both market reaction measures the primary earnings per share cue is most significant. The abnormal trading activity market reaction is driven by the abnormal price reaction with no significant reciprocal causality. This dissertation is dedicated in loving memory of my grandparents, Elmer and Versia Ferrell. ii ACKNOWLEDGEMENTS Without many sources of support and assistance this dissertation would not exist. I greatly appreciate the financial support provided by the Accounting Department at Michigan State University and the Ernst and Whinney Foundation. My dissertation committee devoted themselves to this project and two members, Randall Hayes, chairman, and Kenneth Janson, provided assistance far greater than my expectations. My wife, Patricia, has contributed extensively to this achievement. To these people and all others who assisted me in this project, I extend my sincere gratitude. Thank you. iii TABLE OF CONTENTS LIST OF TABLES ... . . . . . . . . . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . . . . . . . Chapter I I IMRODUCTION O O O O O O O O O O O O O O O O O O 0 Purpose of the Research . . . . . . . . . . Research Paradigm . . . . . . . . . . . . . . . Organization of the Study . . . . . . . . . . . II. THE ROLE OF ACCOUNTING DATA IN SECURITY PRICING . Use of Accounting Data from a Portfolio Perspective Previous Research Evidence . . . . . . . . . . . Empirical Similarity of Accounting Ratios . . Information Content of Financial Accounting Information . . . . . . . . . . . . . . Links Between Accounting Data and Security Rates of Return . . . . . . . . . . . . . . Prediction of Bankruptcy from AccOunting Data The Association Between Systematic Risk and Accounting Variables . . . . . . . . . . . . Behavioral Studies of the Use of Accounting Data . III} HYPOTHESIZED MODEL . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . Information Cues . . . . . . . . . . . . . . . . Market Reactions . . . . . . . . . . . . . . . Hypothesized Relationships Between Financial Dimension Expectation Errors and Market Reactions IV. STATISTICAL METHODOLOGY . . . . . . . . . . . . Causal Modeling . . . . . . . . . . . . . . . . Parameter Estimation and Model Testing . . . . . V. DATA ANALYSIS . . . . . . . . . . . . . Sample Determination: Time Frame and Firms . Expectations . . . . . . . . . . . . . . . . . . Market Reactions . . . . . . . . . . . . . . Data Summary . . . . . . . . . . . . Confirmatory Analysis of Hypothesized Model iv vi vii UN!“ 12 13 19 20 23 24 25 26 26 26 31 35 40 40 41 49 49 50 51 52 SS Exploratory Analysis of Measurement Models . . . . . Exploratory Analysis of Prediction Models . . . . . Exploratory Analysis of Prediction Models Based on the Measurement MOdel M Exploratory Analysis of Pred on the Measurement Model M3 Analysis Assuming Fixed X . Empirical Conclusions . . . Iction Models Based I O I C O O O O O O 0 VI. SUMMARY, CONCLUSIONS, AND IMPLICATIONS . . . . . . . APPENDIX APPENDIX APPENDIX APPENDIX APPENDIX APPENDIX APPENDIX APPENDIX APPENDIX APPENDIX APPENDIX BIBLIOGRAPHY Summary . . . . . . . . . . Conclusions . . . . . . . . Implications . . . . . . . . Recommendations for Future Research . . . . . . . . A B LISREL terminology . . . . . . . . . . . . . . . . 2 X test in the analysis of 8 true tures O O O O O 0 Sample Firms . . . . . . Parameter specifications Parameter specifications measurement model . . Parameter specifications Parameter specifications Parameter specifications Parameter specifications Parameter specifications for for for for for for for covariance hypothesized model . hypothesized measurement model M2 prediction model P1 . prediction model P2 . prediction model P3 . prediction model P4 . Lower left triangle of correlation matrix for coefficients of saturated model: Fixed X- MOdel 14 o o o o o o o 67 76 76 87 90 114 116 116 118 119 120 122 124 .126 128 130 132 134 135 136 137 138 139 10. 11. 12. l3. 14. 15. l6. l7. l8. 19. 20. LIST OF TABLES variables of Stevens' Study . . . . . . . . . . . . Stevens' Study - Factor Analysis Results . . . . . . Stevens' Study - Factor Loadings . . . . . . . . . Johnson's Study Facotr Loadings . . . . . . . . . . . Results of Nerlove Study . . . . . . . . . . . . . . Summary of Data . . . . . . . . . . . . . . . . . . Lower Left Triangle of the Correlation Matrix of the Variables of Analysis . . . . . . . . . . . . . . . Estimates of Parameters for Hypothesized Model . . . Estimates of Parameters for the Hypothesized Measurement Model . . . . . . . . . . . . . . . . . Squared Correlation Matrix for X Variables . . . . Parameter Estimates for Exploratory Measurement Madel M2 0 O I O O O O O O O O I O O O O O O O O 0 Parameter Estimates for Prediction Model Pl . . . . . Parameter Estimates for Prediction Model P2 . . . . . Lower Left Triangle of Parameter Estimates Correlation Matrix for Prediction Model P2 . . . . . . . . . . Parameter Estimates for Prediction Model P3 . . . . . Parameter Estimates for Prediction Model P4 . . . . T-Values of Parameter Estimates for Structural Models Assuming Fixed X . . . . . . . . . . . . . . . . Parameter Estimates for Price Reaction Links for Fixed x - MOdE]. 13 o o o o o o o o o o o o o e 0 Parameter Estimates for Volume Reaction Links for Fixed X - Model 13 . . . . . . . . . . . . . . . Results of Effect Analysis on Fixed X - MOdel 13 . vi Page l3 14 15 16 21 53 54 57 64 68 7O 78 81 83 86 89 109 110 111 113 Figure 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. LIST OF FIGURES Abnormal Performance Experiment Paradigm API Research Paradigm; Information Content Investigation . . . . . . . . API Research Paradigm; Expectation Model Investigation . . . . . . . . . . . . . API Research Paradigm; Cue Usage Investigation . . Hypothesized Measurement Model . . . . . . . . . . Hypothesized Prediction Model . . . . . . . . . . . Hypothesized Causal Model . . . . . . . . . . . . . Hypothesized Causal Model . . . . . . . . . . Hypothesized Measurement Model . . . . . . . . . . Exploratory Measurement Model M 2 . . . . . . . . . Exploratory Measurement Model M3 . . . . . . . . Exploratory Prediction Model P1 . . . . . . . . . . Exploratory Prediction Model P2 . . . . . . . . . . Exploratory Prediction Model P3 . . . . . . . . . . Exploratory Prediction Model P4 . Fixed X - Model 1 . . . . . . . . . . . . . Fixed X - Model 2 . . . . . . . . . . . . Fixed X - Model 3 . . . . . . . . . . . . . . . . . Fixed X - Model 4 . . . . . . . . . . . . . . Fixed X - Model 5 . . . . . . . . . Fixed X - Model 6 . . . . . . . . . Fixed X - Model 7 . . . . . . . . . . . . vii Page 30 37 38 56 63 69 74 77 80 85 88 93 94 95 96 97 99 100 Figure 23. 24. 25. 26. 27. 28. 29. Fixed Fixed Fixed Fixed Fixed Fixed Fixed Model 8 Model 9 . Model 10 Model 11 Model 12 Model 13 Model 14 viii Page 101 102 103 104 106 107 108 CHAPTER I Introduction Purpose of the Research In previous research, Benston (1967), Ball and Brown (1968), Beaver (1968), Brown (1970), May (1971), Brown and Kennelly (1972), Kiger (1972), Hagerman (1973), Gonedes (1974, 1975), Beaver, Clarke, and wright (1979) and others have investigated the reactions of the securities market to the announcement of corporate financial accounting information. The financial accounting information cue investigated was the earnings per share datum. Evidence indicates the market reacts to the announcement of the earnings per share figure. Earnings per share is recognized as having information content, a statistical dependency between earnings per share expectation errors and abnormal security returns and/or trading volume. However, little evidence concerning the roles played by other financial information cues in the securities market's information usage process is available. This research project investigates the use of the financial cues derived from the announcement of earnings and the issuance of the financial statements. A financial cue is a potential stimulus of invest- ment behavior derived from the difference between expected and actual financial results. A specification of the process by which capital markets use various types of financial data is a necessary prerequisite for understanding the interaction of accounting as an information system and the capital market as a user of information. Modeling the relationship between vari- ous types of financial information and the reaction of the security mar- ket to the announcement of the cues allows assessment of the importance 1 2 each of these cues play in setting relative prices. Since both prics and volume reactions are studied, the relationships between the cues and the effects on the market are analyzed from both an individual's and a total market point of view. This is very important to the understanding of the use of information by individuals and by the total market. Research Paradigm The abnormal performance research paradigm is employed in this study. A graphical depiction of the abnormal performance experimental design, adapted from Patell (1979), follows. Investor ’ Event Signal(s) (unobservable) \ A as \\ Economic Accounting I | .y Security States ....c’ Information : : Prices System I I 1 w v ,’ Expectations ‘L Signal(s) Model Event (observable) Figure 1. Abnormal Performance Experiment Paradigm For each firm studied, at a particular point in.time the firm's financial position is depicted by its economic states. Those economic states are characterized by the accounting system where they are recorded and aggre- gated in some form. The accounting system provides a signal or multiple signals concerning these economic states to investors through the announcement of earnings or the issuance of financial statements. 3 The investor event, which is unobservable, contains the revision of expectations due to the signals provided by the accounting system. Since the investor event is unobservable, a representation of the expectations regarding the signal(s) must be formulated. This is the expectations model event. The difference between the expected signal and the actual signal from.the accounting system is the incremental information result- ing from the announcement. From the security prices or returns, a measure of abnormal performance is computed. The traditional use of this paradigm has been to investigate infor- mation content. One assumes: (1) the signal or cue is used by the inves- tor and (2) the expectations model results in a valid representation of the unexpected news resulting from the signal announcement. A measure of abnormal performance is analyzed to infer information content. This use is depicted in Figure 2. Investor Event Infer Information Content Signal(s) (unobservable) I? \ I | E! Economic Accounting Assume I tAssume Security I f i Cue or | |Valid P 1 States n ormat on Signal | |Expectation r ces System Usage | [Models 7\ ,1, 4/ / / Expectations k, Signal(s) Model Event Compute API (observable) Figure 2. API Research Paradigm; Information Content Investigation 4 Patell (1979) demonstrates that if one assumes cue usage and infor- mation content an evaluation of the expectation models can be made. This is shown in Figure 3. Investor Event Assume Information Signal(s) (unobservable) I? Content \ l I E! . Economic Accounting Assume l tEvaluate Security Cue or I |Expectation States Information Signal | [Models Prices System Usage | I 76 .1, .1, ' x / Expectations k, Signal(s) Model Event Compute API (observable) Figure 3. API Research Paradigm; Expectation Model Investigation This research study assumes a valid expectations model and informa- tion content in the announcement of financial data; it investigates the usage of various cues or signals resulting from the release of the firm's financial data. By decomposition of the variation in the abnormal per- formance measures into the components attributable to the variation in the expectation errors of the cues, the usefulness of each cue is inferred. This use of the abnormal performance experimental design is depicted in Figure 4. Signal(s) Economic Accounting States Information System Signal(s) Figure 4. Organization of the Study Investor Event Assume Information C t t (unobservable) l? on en \ I 3 E! Evaluate! |Assume Security Cue or | |Valid P i Signal I |Expectation r ces Usage . IModels 7A .1, 4/ I / Expectations 2’ Model Event Compute API (observable) API Research Paradigm; Cue Usage Investigation Based upon theoretical reasoning and previous research evidence, a causal model is formulated linking the expectation errors of the various cues and the resulting abnormal price and volume reactions of the secur- ities market. cues are estimated and tested. configuration is made. and tested. The parameter coefficients associated with each of the An overall test of the hypothesized model Based upon these results the model is respecified Chapter II contains a discussion of the role of accounting data in security analysis and investment decision making. Previous research cone cerning the relationships among the variables in the hypothesized causal model is reviewed and implications for this study are discussed. Chapter III describes the components of the hypothesized causal model. The relationships among the variables are described and explained. 6 Chapter IV discusses the research methodology employed. A description of the causal modeling technique is provided and the proce- dures for paramater estimation, parameter testing, and model evaluation are discussed. Chapter V contains the data analysis. The research steps employed and an explanation of each step is provided. The results of the parameter estimation and model testing are presented. Chapter VI contains a brief summary of the study. It also includes a list of the major conclusions and implications of this project. Recom- mendations for future areas of study are provided. CHAPTER II The Role of Accounting Data in Security Pricing Use of Accounting_pata from a Portfolio Perspective The role of accounting data in security analysis depends upon the decision context in which the accounting data are used (Beaver, 1981, p. 33). One common decision context for investor decision making is the one period, mean-variance portfolio model. By placing sufficient restric- tions on the preferences and beliefs of the investor, the decision be— havior of the investor is portrayed as if the investor's choice among securities or portfolios is based upon two parameters. These two para- meters are the expected return of the security or portfolio and the vari- ance of that expected return. Although somewhat restrictive, this decision context describes a variety of investor types; diversified, non- diversified, active, and passive (Beaver, 1981, p. 33). Concerning the role of accounting in a portfolio investment context, Beaver (1981, pp. 33-35) notes three pertinent aspects of portfolio theory. 1. The consequences of concern of the investor are characterized as the expected return and the variance of the return of the portfolio. The attributes of the returns of individual securities are relevant only in so far as they contribute to the expected return or risk of the portfolio. 2. A portion of the variance of individual securities' returns can be diversified away, and therefore the variance of the portfolio return is not merely an average of the variances of the securities' returns that comprise it. 3. The security-specific information of interest to the investor will vary in a manner related to the portfolio strategy chosen. In this context, the role of accounting information is potentially to alter the investor's beliefs regarding the expected return and variance 8 of return for all feasible portfolios. These two portfolio parameters are functions of the expected return on the individual securities, the variance of the return for the individual securities, and the covariance among returns of the individual securities that comprise the portfolio (Beaver, 1981, p. 34). The return of an individual security can be decomposed into system- atic and unsystematic components. Utilizing the market model (Fans, 1976), the systematic component reflects that portion of the security return that is linearly related to the return on a "market portfolio." After removing the systematic portion of the security's return the resi- dual or unsystematic portion remains. This relationship is depicted as: (Fame, 1976, p. 100) R1 - oi + 81 Rm + Ui where: R is the return on security i. i R.m is the return on the market portfolio. U1 is the unsystematic portion of the return for security i. + 81 R is the systematic portion of the return for security i. is the intercept of the linear relationship between the return of security i and the return of the market portfolio. is the slope of the linear relationship between R1 and Rm. Bi 81’ a measure of a security's systematic volatility, is dependent upon the extent to which the returns of the individual security covary with the market returns. 8 0(R1, Rm) = E(R1 Rm) - E(Ri) E(Rm) 02(Rm) 02(Rm) where: 0(Ri’ Rm) is the covariance between R and Rm. 1 02(Rm) is the variance of the market return. The variance of the return on security i is equal to the sum of the variances associated with the systematic and unsystematic components of the return. 02(R1) - 812 02(Rm) + 02(U1) 02(n1) - 0(Ri, Rm) 2 02(Rm) + °2(Ui) 2 o (Rm) The relevant investor beliefs regarding the two parameters in the one period, mean-variance portfolio model are: l. the mean return on the market portfolio, E(Rm) 2. the variance of returns on the market portfolio, 02(Rm) 3. the intercept of the security's linear relationship with the market return, 01 4. the slope of the security's linear relationship with the market return, 81 S. the variance of the unsystematic return, 02(U1) 6. the covariance among the unsystematic returns for securities 1 and j, 0(U1, U ) .1 Useful information to the investor provides a basis for the investor to alter or validate his or her beliefs concerning these parameters. In regards to firm specific information, only the a1. 81’ 02(U1), and a (U1, Uj) parameters are affected. For the diversified investor, only information that alters the beliefs concerning the systematic portion of the security return, oi and Bi’ is useful. The potential role of firm specific data is to alter the investor's beliefs concerning the 10 covariation of the security return and the return of the market index. Data that alter beliefs concerning the covariation of security and market returns, the unsystematic return, U1, and the covariation among the un- systematic returns for securities 1 and j, 0(Ui, U ), is useful to the j undiversified investor. Ohlsen (1979) provides an analytic model relating accounting infor- mation to security prices. He examines security valuation relative to the stochastic behavior of accounting numbers and develops this valuation function: (p. 334) N Pt I A + E B X +cn 1.1 1 it t where: Pt is the price of the security at time t. -§t - (Xit’ th,...., Xnt, Dt) is a vector of datum concerning the economic attributes of the firm at time t. X1t denotes financial accounting numbers that represent the economic attributes of the firm at time t. Dt is dividends paid at time t. A, 31’ B2,...., Bn’ C are the valuation parameters obtained by solving a system of simultaneous equations. Ohlsen does not stipulate the accounting numbers to be used. In- stead he asserts (p. 318), "the fundamental characteristics of financial variables are their (joint) stochastic time-series behavior. . . infor- mation variables in this mode of analysis can be any type of variable that affects investors' expectations about future events." The role of financial accounting data in the one period, mean variance portfolio theory investment context is apparent. Any financial variable that has a noneorthogonal relationship with the return stream of the security can be useful to the decision maker. 11 The number of data items inherent in financial reporting is very large. In many cases, these items are highly interrelated and purport to measure the same economic attribute of the firm. The approach of this study, adapted from Ohlsen (1979, p. 317), "stipulates the existence of 'real' economic variables and then uses accounting data as estimates of the real variables." Lev (1974, p. 12) and Foster (1978, p. 28) suggest that four different economic dimensions of a firm are considered in evaluating a firm's performance. Van Horne (1980, pp. 710-713) and Weston and Brigham (1972, pp. 17-19) assert that the liquidity, leverage, profit- ability, and efficiency or activity dimensions are used to evaluate the financial condition and performance of a firm. In security analysis the investor uses these four economic dimensions of a firm to help formulate expectations of future returns. These expected returns are then utilized in the determination of a value for the security. A Let: -§it denote a vector of expected returns for security i at time t. LIit is the liquidity dimension of firm i at time t. LEit is the leverage dimension of firm i at time t. PRit is the profitability dimension of firm i at time t. ACit is the activity dimension of firm i at time t. The expected returns for security i at time t are contingent on the economic dimensions at time t, given a covariation between each dimension and the return series. Therefore: I f(LIit, LE PR , Acit) 3‘11: it ’ it By substitution into the market model, the role of accounting information (surrogates for the four underlying economic dimensions of the firm) in the two parameter, one period, mean-variance portfolio model for a single security portfolio is expressed as: 12 fiit I u + o [EiICLIit’ LEit’ PRit’ Acit)’-§m] Rmt+ Ut 02 (Rm) Expected Variance of Return; 02(Rit) _ o L§i|(LIit, LEit’ PRit, ACit),_§m] 2 02(Rm) + 02(U1) 02(Rm) Assuming; 0R1, L11 # 0 0R1, LE1 # O 0R1, PR1 i 0 0R1, AC1 f 0 Previous Research Evidence Previous research related to the use of accounting data in an in- vestment context can be divided into six categories. The first category consists of studies investigating the empirical similarity of various accounting ratios. The second category contains studies of information content and the third category investigates the relationship between financial accounting variables and the rate of return on securities. Studies concerning the link between financial data and bankruptcy comprise the fourth category.. The fifth category is the relationships between accounting variables and beta while the sixth category contains studies of the use of various accounting data in behavioral contexts. The intent of this literature review is to provide a summary of previous research that is pertinent to this research project. Although not exhaustive, this review provides examples of research previously con- ducted, the results, and the implications of these findings to this project. l3 Empirical Similarity of Accounting Ratios The degree to which financial accounting ratios are indicators of various underlying economic dimensions of the firm has been researched by Stevens (1973) and Johnson (1979). Stevens (1973) employed twenty finan- cial ratios in an exploratory principal components analysis. The twenty ratios and their purported underlying financial dimensions are presented in Table 1. Table 1 Variables of Stevens' Study (Stevens, 1973, p. 151) Purported underlying Ratio Dimension Number Ratio Liquidity 11 net working capital/total assets 17 net working capital/sales Profitability 1 EDIT/total assets 5 gross profit/sales 6 EBIT/sales 7 net income/sales 8 EDT/sales 9 net income/net stockholders equity 10 net income/total assets Leverage 4 long-term (LT) debt/market value equity l8 LT debt/total assets 13 LT debt/net stockholders equity 19 LT liabilities/total assets 20 total liabilities/total assets Activity 16 sales/total assets 15 cost of goods sold/inventory 14 sales/(current assets - inventory) "Other" 12 interest/(cash + marketable securities) ' 2 cash dividends/net income 3 price/earnings The results of Stevens' study, factors, eigenvalues, and percentages of variance explained, are provided in Table 2. 14 Table 2. Stevens Study-Factor Analysis Results Percent Variance Cumulative Percentage Factor Eigenvalue Explained of Variance Explained 1 6.46 32.32 32.32 2 3.72 18.60 50.92 3 2.49 12.47 63.40 4 1.67 8.38 71.78 5 1.15 5.75 77.54 6 0.99 4.95 82.49 7 0.79 3.97 86.47 8 0.65 3.26 89.74 9 0.52 2.64 92.39 10*. 0.44 2.24 94.63 *The remaining factors were omitted from this table and accounted for only 5.37 percent of total variance. ’ 15 The loadings of the ratios on six factors resulting from a varimax rotation are presented in Table 3. Table 3. Stevens Study-Factor Loadings Factor 4 .888 13 .933 18 .937 19 .927 20 .815 1 .908 6 .787 8 .781 9 .784 10 .751 14 .794 16 .850 11 .842 2 .811 l .896 NOTE: Factor loadings less than .7 were omitted, and variables 5, 7, 12, 15, and 16 do not have loadings high enough to be included in the table. These results indicate that the ratios representing leverage, profit- ability, and (to some extent) the activity dimension do possess high de- grees of concomitant variation. 'As such, the validity of these ratios as measures of the associated financial dimension is warranted. However, since Stevens omits any loadings less than .7, it is very difficult to assess the degree to which the ratios loaded on multiple factors. Johnson (1979) conducted a factor analysis on sixty-one financial ratios using eight factors. His results (p. 1038-1040), presented in Table 4, indicate that some ratios loaded on more than one factor. This implies that some of the ratios may not be good indicators for the under- lying financial dimensions. 16 The results of these studies indicate that a measurement model com- prised of ratios as indicators of the four underlying financial dimensions is warranted. However, the existence of some ratios loading on more than one factor indicates that a high degree of covariability may exist between indicators of different dimensions. Both the Stevens (1973) and the Johnson (1979) studies failed to test the adequacy of fit for their factor analytic models. Given the degree of covariability among the indicators of different dimensions, the ability to find an adequate measurement model configuration that is interpretable may be difficult. Table 4. Johnson Study Factor Loadings Factor Loadings . 1972 1974 Ratio Primary ' Primary Number Ratio Name Mfg. Retail Mfg. Retail FACTOR 1--RETURN 0N INVESTMENT 4 Earnings/Sales .88 .63* .75 .81* 7 Earnings/Net Worth .79 .94* .95 .95* 12 . Earnings/Total Assets .93 .89* .85 .87* 13 Cash Flow/Total Assets .92 .85* .84 .84* 14 Cash Flow/Net Worth .50 .88* .79 .93* 15 EBIT/Total Assets .89 .85* .77 .84* 16 EBIT/Sales .89 .61* .70 .77* 17 Cash Flow/Total Capital .94 .90* .85 .93* 18 Earnings/Total Capital .94 .90* .88 .94* 19 Cash Flow/Sales .79 .59* ' .87 .74* 41 EBIT/Net Worth .798 .92* ,.95 .97* 47 Cash Flow/Total Debt .81 .73* .84 .70* 48 Earnings/Total Debt .87 .78* .86 .73* 53 Operating Funds/Total Assets .88 .82* .45 .82* 54 Operating Funds/Net Worth .25 .75 .63a .86 55 Operating Funds/Total Capital .83 .81 .33 .88 FACTOR 2-FINANCIAL LEVERAGE 2 Net worth/Total Assets -.80 -.85* -.82 -.693* 5 Long Term Debt/Total Assets .87 .85 .85 .87 11 Long-Term Debt/Net Worth .88 .90 .91 .93 29 Long-Term Debt/Net Plant .85 .81 .80 .81 30 Long-Term Debt/Total Capital .89 .92 .94 .91 31 Total Debt/Net Worth .79 .85 .83 .71a 32 Total Debt/Total Assets .81 .85* .79 .74* 50 Total Debt and Preferred Stock/Total Assets .79 .85* .78 .68* Table 4. Continued 17 Factor Loadings 1972 1974 Ratio Primary Primary Number Ratio Name Mfg. Retail Mfg. Retail FACTOR 3-CAPITAL INTENSIVENESS 3 Sales/Net Worth .66 .85* .70a .78* 6 Sales/Total Assets .788 .81* .75 .79* 19 Cash Flow/Sales -.44 -.723* -- - 20 Current Liabilities/Net Plant .81 .49* .81 .43a 22 Current Assets/Total Assets .88 .46* .84 .41 26 Sales/Net Plant .94 .78* .91 .79* 27 Sales/Total Capital .85 .91* .86 .83* FACTOR 4--INVENTORY INTENSIVENESS 1 Working Capital/Sales .72a .44* .69a .81* 20 Current Liabilities/Net Plant .33 .71* -- -— 21 Working Capital/Total Assets .40 .76 .46 .85 22 Current Assets/Total Assets ' .39 .83* .45 .84 24 Current Assets/Sales .92 .74* .92 .74* 25 Cost of Goods Sold/Inventory -.91 -.92* -.94 -.93* 28 Inventory/Sales .87 .93* .94 .93* FACTOR 5-CASH POSITION a2 Cash/Total Assets .91 . 93 .39 .81. 43 Cash/Current Liabilities .84 .88 .83 .87 44 Cash/Sales .93 .88* .89 .90* 46 Cash/Fund Expenditures .91 .86* .88 .89* FACTOR 6-RECEIVABLES INTENSIVENESS 23 Quick Assets/Total Assets .52 .89* .68a .89* 33 Receivables/Inventory .94 .84* .80a .82* 34 Inventory/Current Assets -.758 -.70* -.64 -.76* 35 Receivables/Sales .72a .83* .81 .83* 37 Quick Assets/Sales .58 .86* .78 .88* 40 Quick Assets/Current Liabilities .40 .76* .46 .81* 45 Quick Assets/Fund Expenditures .55 .85* .75 .87* FACTOR 7--SHORT-TERM LIQUIDITY 21 Working Capital/Total Assets -- - .73 -.35 36 Inventory/Working Capital -- -- -.79 .16* 38 Current Liabilities/Net Worth -- - -.55a .80 39 Current Assets/Current 40 Quick Assets/Current 49 Current Liabilities/Total Assets -- -- -.64a .78* 51 Net Defensive Assets/Fund Expenditures .55 .74* .75 -.523* 18 Table 4. Continued Factor Loadings 1972 Ratio Primary Primary Number Ratio Name Mfg. Retail Mfg. Retail FACTOR 8-DECOMPOSITION MEASURES 56 Asset Decomposition .68 .74 - -- 58 Equity Decomposition .84 .84 .86 .87 60 Noncurrent Items Decomposition - .83 .78 .87 .85 61 Time Horizon Decomposition - -- .62 .70 aIndicates variables having a within-sample cross-loading of between .50 and .70 on one other factor. a t-test of untransformed data significant at p < .05. 19 Information Content of Financial Accounting_Information Many researchers have investigated the information content of corporate earnings announcements. Benston (1967), Ball and Brown (1968), Brown (1970), May (1971), Brown and Kennelly (1972), Hagerman (1973), Gonedes (1974, 1975), and others have found evidence indicative of a market reaction to the announcement of earnings. Beaver (1968) and Kiger (1972) studied both price and volume reactions associated with the announcement of earnings; both reactions were found to be significant. The relationship between the magnitude of change in expectations re- garding earnings and the magnitude of abnormal price reactions has been investigated by Beaver, Lambert, and Morse (1980) and Beaver, Clarke, and Wright (1979). The former project found a correlation of .49 between per- centage changes in security prices and percentage changes in expected earnings at the individual firm level. Beaver, Clarke, and Wright found similar evidence with a .38 correlation. The remaining unexplained vari- ation (.76 and .86) is attributed by Beaver (1981) to other firm events beyond the profitability measure. Other cues resulting from financial reporting may be linked to the market reactions. Gonedes (1974) used discriminant analysis to find significant links between abnormal returns and measures of liquidity, leverage, profitabil- ity, and activity. The forecast errors associated with the following ratios were used in his empirical analysis (p. 52). 1. (current assets - current liabilities)/(total assets) 2. (common equity)/(total assets) 3. (operating income)/(tota1 assets) 4. earnings per share 5. (total assets)/(sales) 20 6. (net income)/(tota1 assets) 7. (net income + depreciation + amortization)/(preferred stock + long term debt + current liabilities) Gonedes (p. 49) states, "The results of our multivariate tests assign a high probability to the statement that the numbers do jointly provide information pertinent to assessing equilibrium expected returns." The results of these studies imply that data regarding the liquidity, leverage, profitability, and activity dimensions possess information content. Therefore, the information cues regarding these dimensions are used by the investor market. Cue usage is a necessary but not a suffi- cient condition for information content to be inferred. This research project investigates cue utilization for an expanded set of financial ratios in order to assess the apparent usefulness of various financial ratios and financial dimensions to investors. Links Between Accounting Data and Security Rates of Return Using multiple regression, Nerlove (1968) regressed rates of return on eight accounting variables for a sample of three hundred-seventy one firms. He tested three five-year periods and one fifteenryear period. His results (p. 324) are provided in Table 5. 21 Table 5. Results of Nerlove Study Variable rate of sales growth rate of earnings growth retained earnings/ total assets dividends/total assets reciprocal of leverage inventory turnover share turnover gross plant/total assets 'Period 1950-1954 1955-1959 1960-1964 1950-1964 .196 .336 .469 .157 t-3.54 t=6.56 t-6.33 t=2.74 .076 .032 .015 .0094 t-4.28 t-3.26 t-3.20 t-2.64 2.105 2.075 1.253 2.022 t-10.20 t-10.20 t-5.06 t=12.26 .278 .240 .226 .225 t-1.72 t-1.l8 t-1.03 tsl.95 -0046 -0020 -0061 -0066 t-2.05 t-.75 t-1.90 t-3.98 -.0017 -.0056 -.0024 -.0003 t-4.08 t-1.25 t-2.85 t-.96 .044 .138 -.021 .0035 t-2.13 t-6.38 t-.85 t-.25 .010 -.060 -.0034 -.028 t-.90 t=4.92 ta.24 t-4.14 .425 .515 .280 .493 Martin (1971) regressed earnings to price ratios on eight accounting variables. The ratios and their significance in explaining the variation in the earnings to price ratios are: 22 Ratio Stability of Sales Over Time Growth in Operating Cash Flow Over Time Payout Ratio Operating Income/Sales Net Income/Common Equity Total Assets Capital Expenditures/Sales Cash Flow/(Long-Term Debt & Preferred Stock) Significant at q:.05 No Yes No Yes Yes No No Yes The results of the Nerlove study and the Martin study indicate a stochastic relationship among accounting ratios that are indicators of underlying financial dimensions and rates of return. O'Connor (1973) re- gressed various forms of the rate of return on averaged ratios. The ratios he employed were: 1. total liabilities/net worth 2. working capital/sales 3. sales/total assets 4. income available to common shares/common equity 5. income per share after dividends/income per common share 6. pretax net nonoperating income/sales 7. net income/net income before taxes 8. cash flow/number of common shares 9. current liabilities/inventory 10. earnings per share/price per share He found that (1), (4), (8), (9), and (10) were significant (a - .05) in explaining the variation in the rate of return variable. However, 23 O'Connor concluded (p. 350), "tests of predictive ability over time pro- vided no evidence that the explanatory relationships were useful in pre- dicting future rate of return rankings." These results indicate that a relationship exists between current period accounting ratios and current period rates of return. This is consistent with the idea that information regarding these ratios or the financial dimensions they represent is important to the investor for determination of expected returns. Prediction of Bankruptcy from Accounting;Data A recent study by Ohlsen (1980) investigates the prediction of bank- ruptcy from these financial ratios: 1. size 2. total liabilities/total assets 3. working capital/total assets 4. current liabilities/current assets 5. indicator variable if total liabilities exceed total assets 6. net indome/tbtal assets 7. operating income/total liabilities 8. indicator variable if net income was negative for the last two years 9. change in net income Using maximum likelihood estimation of the conditioned logit model, Ohlsen identified four basic factors statistically significant in affec- ting the probability of a failure within one year. These dimensions were company size, leverage, profitability, and liquidity. Altman (1968), using discriminant analysis, found links between firm failure and indi- cators of liquidity, profitability, and leverage. 24 These findings indicate that financial accounting data, which are indicators of liquidity, leverage, and profitability, are potentially useful to the investor. The Association Between Systematic Risk and Accounting Variables Lev (1974a, p. 105) stresses that the risk of a firm is determined by the financial and operating characteristics of that firm; financial statement data should be linked to beta. Empirically, Roenfeldt and Cooley (1975) used canonical correlation analysis and found both excess returns and risk functionally related to liquidity, leverage, and size. Simkowitz and Logue (1973) demonstrated that a relationship exists between profitability, leverage, and beta. Ramada (1972, p. 451) found twenty- one to twenty-four per cent of the variation in systematic risk explained by leverage. Bowman (1979) analytically provides a theoretical basis for rela- tionships between systematic risk and financial accounting variables. He shows that a theoretical relationship exists between a firm's systematic risk and the firm's leverage and accounting beta. Also, Hamada (1972) demonstrates that systematic risk is not theoretically related, in a direct manner, to earnings variability, dividends, firm size, or rate of. firm growth. However, any accounting variable that is related to the covariability of the firm's earnings and the market's earnings is indi- rectly related to the systematic risk of the firm. The results of these studies provide evidence that accounting data is related to the systematic risk of a firm. Since the systematic risk parameter is an important part in the one period, mean-variance portfolio investment model, accounting data that is related to systematic risk is pertinent to the investor. 25 Behavioral Studies of the Use of Accounting Data Abdel-Khalik and El-Sheshai (1979) found that lending officers choose profitability, liquidity, and leverage information for predicting default. Pankoff and Virgil (1970) also found profitability, leverage, and liquidity information useful to security analysts. Mayer-Sommer (1979) surveyed Certified Financial Analysts and found that ninety-nine per cent of the respondents believe that analysis of a firm's operating and financing characteristics is used in investment analysis. Financial accounting statements, both audited and quarterly, were found to be used by ninety-three per cent of the respondents. In a behavioral study, Gooding (1978) used multidimensional scaling to find that risk perceptions are multidimensional. He established that company operating and financ- ing characteristics are used by investors to calculate expected returns. Empirical research has found profitability data, earnings per share, to possess information content. Research has not been conducted on the usefulness of accounting cues regarding liquidity, leverage, profitabil- ity, and activity attributes of a firm. This is surprising since the pertinence of accounting data to the investor has been demsnstrated through analytical and empirical research linking accounting data to security rates of return, bankruptcy, and systematic risk. This study directly investigates the use of accounting data in a market study. Causal links between expectation errors regarding the four financial di- mensions of a firm and two measures of market reactions, abnormal trad- ing and abnormal returns, are hypothesized and tested. CHAPTER III Hypothesized Model Introduction The relationships between information cues, resulting from the announcement of accounting data, and the associated security market re- actions are modeled in this study. In order to operationalize this study, three components are needed. They are the cues, the market reactions, and the framework of hypothesized relationships between the cues and the market reactions. Each of these components is presented and discussed in the following sections. Information Cues A cue, which may vary in type and intensity, is the link between the perception of a stimulus and the response. An announcement of earn- ings or other financial data is a stimulus; it produces cues to the ex- tent that expectations of firm attributes, deemed pertinent for investment decisions, change or are realized. According to Beaver (1981a, p. 36), financial datum becomes information when it alters beliefs about security specific parameters. The expectation errors for the liquidity, leverage, activity and profitability dimensions, prompted by the announcement of accounting data, are the cues to be investigated in this study. These expectation errors are the differences between expectations of the dimensions prior to the release of the accounting data and the realizations of these dimensions given the publication of the accounting data. Although these dimensions can be defined, they are unobservable con- structs representing the financial and operating aspects of an economic entity. Mock (1976, p. 27) suggests the use of observable surrogates or 26 27 indicators as measures of unobservable constructs. The basic model of this approach is: (Meck, 1976, p. 52) Xt B it + 6t where: Xt - the observed number of score which is assigned as the magnitude of the attribute of interest on the tth assignment. 6 = the unobservable true magnitude of the attribute. 6 - an unobservable error component. t I l, 2, . . . t represents replications (of the measure- ment process or of objects measured). It is assumed: (l) the relationship is stable. (2) the error component is a random variate which is dis- tributed independently of the true score. (3) the measurement errors, at, are additive to the true score. Since it is not possible to observe the four economic dimensions of a firm, certain measurement devices or surrogates must be used. ‘The common measurement devices or surrogates used in financial analysis are financial ratios. Following are the four unobservable financial dimen- sions and the measures of each used in this project: Liquidity Current Ratio - Current Assets/Current Liabilities Quick Ratio - (Cash + Marketable Securities + Receivables)/ Current Liabilities Defensive Interval - (Cash + Marketable Securities + Receivables)/(Expenditures + 365) Leverage Total Debt to Equity Ratio - Total Debt/Total Equities Long-Term Debt to Equity Ratio - Long Term Debt/Total Equities Times Interest Earned - Income before Interest and Taxes/ Interest 28 Profitability Return on Assets - Net Income/Average Total Assets Earnings to Sales Ratio - Net Income/Net Sales Primary Earnings Per Share Return on Common Stock Equity - Net Income after Preferred Dividends/Common Equity Activity Asset Turnover - Net Sales/Average Total Assets Receivable Turnover - Net Sales/Average Net Receivables Inventory Turnover - Cost of Goods Sold/Average Total Assets The choice of the ratios hypothesized to be indicators of the unob- servable financial dimensions is based upon an analysis of textbooks in accounting and finance including Foster (1978, p. 28), Kieso and Weygandt (1977, p. 1020), Van Horne (1980), Weston and Brigham (1972), Schall and Haley (1980, pp. 390-391). The expectation errors regarding the underlying financial or economic dimensions of a firm and the expectation errors regarding the observable measures of the four dimensions comprise the measurement model portion of the hypothesized causal model. Let: - expectation error regarding the liquidity dimension - expectation error regarding the leverage dimension - expectation error regarding the profitability dimension - expectation error regarding the activity dimension X - expectation error of the current ratio x - expectation error of the quick ratio x - expectation error of the defensive interval x - expectation error of the long term debt to equity ratio x - expectation error of the total debt to equity ratio x - expectation error of the times interest earned ratio x a expectation error of the return on total assets x - expectation error of the earnings to sales ratio x - expectation x10 - expectation X11 . expectation x12 - expectation x13 - expectation A - measurement measure and 29 error or primary earnings per share error of the return on equity error of the total asset turnover error of the accounts receivable turnover error of the turnover ratio coefficient between the observable the underlying/unobservable financial dimension expectation error 6 to 6 - the associated measurement error 1 13 The hypothesized measurement model is: XI), 1 11 51 + x2 ' x12 51 + x3 ' A13 51 + x4 ' X21 g2 + x5 ‘ A22 a2 + x6 ' 123 ‘52 + x7 ' A31 53 + 1 8 32 8 62 x9 ' A33 53 + 69 63 x10 7 A34 E3 + 610 54 x11 ' A41 54 + 611 65 x12 ’ X42 54 + 612 66 x13 ' x43 54 + 613 57 Figure 5 is a diagrammatic representation of the hypothesized measurement model. The x's represent the observed expectation error which are surro- gates for the expectation errors of the underlying financial dimensions. The 6's represent the measurement error of the observed expectation error as an imperfect measure of the unobservable financial dimension expectation error. The observed expectation error is a composite of the underlying dimension expectation error and the measurement error. 30 0'. H k X H 0' N I) X N m ..o ”On I .2.‘ 0‘ t I X 5' Op 1.» I K 0'! O! \1 I X \J // V V 63 if x8 / £3 69 I: x9 ‘///////’/// 6,0 t X10 611 =-"114\ 512 e: X12: 5% \ O. ... u I X ... u: where it is assumed that the 5's are not orthogonal and may covary. Figure 5. Hypothesized Measurement Model 31 Market Reactions The existence of two types of market reactions has been demonstrated by previous research. Beaver (1968) used both changes in the equilibrhmn value of current market prices and shifts in portfolio positions, reflec- ted in trading volume, to research information content. Beaver (1968, pp. 68-69) remarks, An important distinction between the price and volume tests is that the former reflects changes in the expectations of the market as a whole while the latter reflects changes in the expectations of individual investors. A piece of infor- mation may be neutral in the sense of not changing the ex- pectations of the market as a whole but it may greatly alter the expectations of individuals. In this situation, there would be no price reaction, but there would be shifts in portfolio positions reflected in volume. Isolation of a market reaction due to a specific event requires con- trol of other factors or events occurring concurrent with the specific event being studied. To assess price reactions in this study, a measure based upon the market model will be used. The market model states that the returns of an individual security are a linear function of the gen- eral market factor (Dyckman, Downes, and Magree, 1975, p. 110).' This relationship can be expressed as: (Fama, 1976, p. 100) "b R = a + bi amt + e it i it '0 where: Rit is the return on the ith security at time t amt is the return on the market at time t a and b1 are the regression coefficients 1 ’b eit is the abnormal return or disturbance term 32 It is assumed: ’1) N E— 613 <¢ x13/ Figure 7. Hypothesized Causal Model 39 The thesis of the hypothesized causal model is that all four of the information cue regarding the economic dimensions of a firm are impounded by the market. The reaction of the securities market to the use of the four cues is found in the abnormal return and abnormal volume measures. This model also depicts a causal link between abnormal volume and abnormal returns. A volume reaction results from a change in the price of a security but a price reaction is not prompted by abnormal trading. Since the four economic dimensions of a firm are unobservable, sur- rogates or indicators are employed in security analysis. The common surrogates used are financial ratios. The expectation error regarding the liquidity dimension is represented by the expectation errors for the current ratio, the quick ratio, and the defensive interval. The indica- tors of the expectation errors for the leverage dimension are the expec- tation errors of the long term debt to equity ratio, the total debt to equity ratio, and the times interest earned ratio. The expectation errors for the return on total assets, the earnings to sales ratio, pri- mary earnings per share, and the rate of return on equity are the meas- ures of the profitability dimension expectation error. The expectation error of the activity dimension is represented by the expectation errors for total asset turnover, accounts receivable turnover, and inventory turnover 0 CHAPTER IV Statistical Methodology Causal Modeling A model is a "representation of reality to explain some aspect of it" (Miller and Star, 1969, p. 145 and Montgomery and Urban, 1969, p. 9). Representing the underlying conceptual and theoretical structure, a causal model portrays the causal links and chains between the components of the process researched (Abdel-Khalik and Ajinkya, 1979, pp. 20-23). Causal modeling is unique in its effort to develop a structured network of causal relationships built upon theoretical underpinnings. Causality is important; it is a necessary condition for stating that the exogenous variables generate the changes in the endogenous variables in settings beyond the conditions under which the observations were made (Abdel- Khalik and Ajinkya, 1979, p. 24). This research project intends to ful- - fill the three conditions for establishing causality. These conditions are: (Asher, 1976, pp. ll-12). a. There must be concomitant variation between the variables of interest. b. There must be a temporal asymmetry between the variables of interest. c. Other possible causal factors are either eliminated or controlled. Nonefirm specific events which might affect measures of market re- actions are controlled by using the market model approach to develop the CARs and the CAVs. Any firm specific events other than the exogenous variables of interest are controlled through random selection of the sample firms. The condition of temporal asymmetry is met since financial cue utilization must preclude an associated market reaction. Assessment 40 41 of concomitant variation between the variables of interest will be investigated through empirical analysis. Parameter Estimation and Model Testing To estimate the parameters and test the model, Lisrel: Analysis of Lgnear Structural Relationships by the Method of Maximum Likelihood by Joreskog and Sorbom (1978) is chosen. Appendix A contains a glossary and a description of the notation used in LISREL. Joreskog and Sorbom des- cribe the program: (1978, p. 3) The LISREL model is particularly designed to handle models with latent variables, measurement errors and reciprocal causation (simultaneously interdependence). In its most general form it assumes that there is a causal structure among a set of latent variables or hypothetical constructs some of which are de- signated as dependent variables and others as independent vari- ables. These latent variables are not directly observed vari- ables that are related to the latent variables. Thus the latent variables appear as underlying causes of the observed variables. The hypothesized causal model of this project, n1 ' Y11 51 + Y12 52 + Y13 53 + Y14 54 + Y1 n2 ' Y21 £31 + Y22 a2 + Y23 E33 + Y24 54 - 821 n1 + 51 X1 ' X11 51 + 61 x8 ' A32 53 + 58 x2 ' A12 51 + 62 x9 ' A33 53 + 69 x3 ' A13 61 + 63 x10 ' A34 53 + 510 x4 ' A21 a2 + 54 x11 ‘ A41 54 + 511 x5 ' A22 a2 + 55 x12 ‘ x42 54 + 512 x6 ' A23 52 + 66 x13 ' x43 54 + 513 x7 ' A31 ‘53 + 67 42 is a specified form of the following general model. (Joreskog and Sorbom, 1978, pp. 4-7) .§.fl '.£.§‘+.£ (l) where: I'd Ix J>» where: D. .5 Ion lv-J ‘§> X. lo, In J> J> (mxl) (nxl) (mxm) (mxn) (mxl) D. .g (pxl) (qxl) + is a vector of the latent (underlying/unobservable) endogenous variables is a vector of the latent (underlying/unobservable) exogenous variables is the matrix of causal coefficients relating the endogenous variables to each other is the matrix of causal coefficients relating the endogenous variables to the exogenous variables is a vector of random residuals or prediction errors (2) In + .5. (3) are observations[indicators/measures of the latent endogenous variables 3 are observations/indicators/measures of the latent exogenous variables é (pxm) is a matrix of regression coefficients of Z_on fl (qxn) is a matrix of regression coefficients of §_on g is a vector of measurement errors for X'as measures of.fl is a vector of measurement errors for g'as measures of_§ By assuming that all the variables are mean-deviated: Egg) I 0 EQQ) ' 0 EC!) - 0 E(z) ' 0 5(5) - 0 Egg) - 0 Eflg) ' 0 43 The normal regression assumptions are also assumed: cg; - 0; the prediction errors are uncorrelated with the exogenous variables GEE a O; the measurement errors of y as a measure of n are uncorrelated with n o§§ = 0; the measurement errors of x as a measure of 5 are uncorrelated with 5 deg - 0; the measurement errors of y as a measure of n are uncorrelated with g oéfl - 0; the measurement errors of x as a measure of E are uncorrelated with n as; - cg; - 0; the measurement errors are uncorrelated with the prediction errors However, in the general LISREL model it is assumed that the measurement errors may be correlated among themselves. Let: ¢ (n x n) - covariance matrix of the exogenous variables, E W (m x m) - covariance matrix of the prediction errors, 5 g - covariance matrix of the measurement errors of the endogenous variables 96 - covariance matrix of the measurement errors of the exogenous variables The variance-covariance matrix of the x and y variables created by the specified causal model is (Joreskog and Sorbom, 1978, p. 5): §_((p + q) x (p + q)) - .1 A (3’1 r o r’ 8"1 + 8'1 w B’ 1) A’ + e A ‘1 r ¢ A’ -y -- --— - — —- - -e -y- ---x _1 (4) A o r’ 3’ A’ A o A’ + e -x-- -y -x--x -5 _J 44 In applications of this general model, the elements of Ay’ Ax’ B , I‘ , 3 . 1.§€.and96 depending upon the hypothesized causal structure. are specified to be either free, constrained, or fixed, The measurement model, equations (2) and (3) can be written in fac- tor analytic form as: E'A£+e where: g - (y, _x_) _f_ - (fl: 5) E ‘ (Es 5) A 0 -y — A I O A - -x Therefore, the measurement model is a restricted factor analysis model in which the factors_3 and E satisfy a linear structural equation system of the form: £1-£s+2 By specifying 3 , the covariance matrix of the exogenous variables, to be diagonal, an orthogonal solution is derived. If theag matrix is spec- ified as full rank, an oblique solution is obtained. For additional references on the use of factor analytic techniques in causal modeling see Jackson and Borgatta (1981, pp. 179-281), Judge, Griffiths, Hill and Lee (1980, pp. 550-554), Hanushek and Jackson (1977, pp. 302-324). Before one can estimate the parameters of a causal model it is necessary to establish that the parameters are identified. For a given model specification, the structure denoted by Ay’ Ax’ _§ , I , 3 , i , _0_€ , and _€> 6 generates one and only one variance-covariance matrix, 2: , but there may be numerous structures generating the same §_(Joreskog and 45 Sorbom, 1978, pp. 9-11). Two or more structures that generate the same E_ are equivalent. A parameter that has the same value for all equiva- lent structures is identified. The whole model becomes identified when all of the individual parameters are identified. Let §_be a vector of all the independent, free, and constrained parameters specified by a certain model and let t be the order of g. The problem.of identification is whether or not §_is determinable by 2,. To assess this, consider the equations in (4) of the form: “ij'f 09,151 1.1 There are (1/2) (p + q) (p + q + 1) equations and t unknown elements in ‘g. A necessary condition for identification of all parameters is that: t5—(1/2) (p+q) (p+q+l) The number of estimated parameters must be less than or equal to the number of elements in the lower left triangle of the observed variance covariance matrix for the x and 2 variables. The specified model matrices for the hypothesized causal model of this study and the number of elements to be estimated are as follows: Number of Elements Matrix to be Estimated A O “Y A 13 -x B 1 he be P1 H woos IG) 0 lo 07 lt—I La.) 46 Constraining 5%? such that only the main diagonal elements are estimated and the remaining elements of the lower left triangle are fixed at 0, fulfills the necessary condition for identification. The model is over- identified since 48 51/2 [(p + q) x (p + q + 1)] - 120. This constraint or restriction implies that the measurement errors, 61 through 613, do not covary. No covariance among the measurement error terms presumes that the underlying construct is the only systematic source of variation in the observed indicators. This restriction is come monly employed in traditional factor analytic techniques. For estimation and testing of the model it is assumed that the dis- tribution of the observed variables can be described by the first two moments, a mean vector and the variance-covariance matrix. The estima- tion process comprises fitting the 3;, the covariance matrix constructed by the hypothesized model specifications, to the observed covariance matrix‘g. §_(p+q)x(p+q)- (PXP) (pxq) s s -w -yx §xy (q x p) §xx (q x p) The fitting function: F a log [2} + tr (g Efl) - log I§J - (P + q) is minimized with respect to E3 §_is the set of free, constrained, or equivalent parameters designated by the hypothesized causal model. In minimizing the fitting function, one is minimizing the difference between the generalized variance of the created covariance matrix and the gener- alized variance of the observed covariance matrix. If one assumes that the recreated variance-covariance matrix, §_, equals the observed 47 variance-covariance matrix, S, the determinant of E_, the generalized variance of E , equals the determinant of §_. Hence, log [3' equals log |§_I . Since _3_ - 5 , (_ 3.1.1) is equivalent to an identity matrix of order (p‘+ q). Therefore, the trace of (§_§f1) equals (p + q). The result is F - 0 when the recreated covariance matrix §_equa1s the observed covari- ance matrix S. The hypothesized model structure represents the process which produced the observed covariance matrix. Maximum likelihood estimates, efficient for large samples, result if the distribution of (y, x) is multinormal (Joreskog and Sorbom, 1978, p. 3 and Hanushek and Jackson, 1977, pp. 314-316). The procedure to select the estimates that minimize the F function involves taking the derivatives of the F function, with respect to each parameter estimated, and solving this set of simultaneous equations for the values that equate the derivations to zero (Hanushek and Jackson, 1977, p. 315). For a more complete discussion of the estimation procedure see Joreskog in Gold- berger and Duncan (1973, pp. 85-112). Once the maximum likelihood estimates of the parameter have been obtained, the hypothesized model is tested for goodness to fit. The total model is tested to determine its ability to create a covariance matrix, 3; , that replicates the observed covariance matrix, §_. Let Ho be the null hypothesis representing the total model as specified. The alternative H1 is that §_is any positive definite matrix. The test statistic, NFC, is minus twice the logarithm of the likelihood ratio where F0 is the minimum value of F and N is the sample size. NFo is asymptotically distributed as x2 with degrees of freedom d; d a 1/2 Ep + q) (p + q + 1) - awhere t is the total number of independent para- meters estimated under Ho (Joreskog and Sorbom, 1978, p. 14). Appendix 48 B contains a discussion of the X2 difference test for testing alterna- tive model structures. The hypothesized measurement model will be tested for goodness of fit against the null measurement model. The null measurement model fixes the A's equal to zero. It is important to test the hypothesized measure- ment model. Bentler and Bonnett (1980, p. 604) state, "There may be little point to evaluating a given regression structure if the measure- ment model is totally inadequate." This research project estimates the parameters and tests the model as specified. As warranted, the model is respecified and retested using both the X2 goodness of fit test and the incremental fit index of Bentler and Bonett (1980, pp. 599-600). This incremental fit index denotes the increase in model fit as measured by the change in the generalized vari- ance explained by the hypothesized model. The results of the parameter estimation and model evaluation of the hypothesized causal model are pre- sented in the following chapter. Respecification of the causal model and the appropriate estimation and retesting are also discussed. CHAPTER V Data Analysis Sample Determination: Time Frame and Firms The firms studied are calendar year firms listed on the New York Stock Exchange. The accounting data releases studied are for the year ended December 31, 1979. These releases are the announcement of earnings, the annual report issuance, and the submission of the lO-K report. An initial sample of three hundred firms was randomly chosen from firms that made the earnings announcement during February, 1980 and made public the annual report and the lO-K report prior to March 31, 1980. To be in- cluded in the data analysis, a sample firm met the following conditions: 1. A firm must have complete requisite data on the Compustat yearly data base for 1978 and 1979. 2. A firm must have complete requisite data on the CRSP monthly return data base for the period January 1, 1975 through March, 1980. 3. A firm.must have complete requisite data on the Rapid- quote data base for the period January, 1975 through March, 1980. 4. A firm.must have filed third quarter, 1978 and 1979 10-Q reports with the Securities and Exchange Commission and the reports must be accessible at the Securities and Exchange Commssion Reading Room in Chicago, Illinois. 0f the initial three hundred firms, two hundred and nine met these re- quitements. The Compustat data base contains quarterly and annual finan- cial accounting data. Return data used to develop market price reactions was found on the New York Stock Exchange return data base developed by the Center for Research in Security Prices at the University of Chicago. Data regarding the number of shares traded was obtained from the Rapid- quote data base. Rapidquote is Rapidata's securities data base which 49 50 contains current and historical trading, financial, and descriptive information on approximately twelve thousand securities. Appendix C contains a list of the two hundred and nine firms used for this study. Expectations The observable cues to be investigated are the expectation errors regarding the financial ratios that measure the underlying financial di- mensions. An expectation error is the difference between the expectation of a ratio prior to the release of the accounting data and the realiza- tion of that ratio due to the release of the accounting data. For the expectations of the year end ratios for the 1979 year, the market realizes the data contained in quarterly earnings announcements and quarterly lO-Q reports for the first three quarters. The lO-Q reports must be filed within forty-five days of the end of the quarter. There- fore, the 10-Q report for the third quarter 1979 is made public by the middle of NOvember. The expectations of the annual accounting data items for 1979 are assumed to be a composite of the third quarter data and an estimate of what will happen during the fourth quarter. For the estimate of the results for the fourth quarter the naive model is used: E(thp) ' Qc-a where: Q is the accounting data item in the fourth quarter of 1979 and Qt-4 is the accounting data item in the fourth quarter of 1978. is determined as the difference between the 1978 annual report and the third quarter report of 1978 for the data item. Qt-4 The expectation of an annual accounting datum is expressed as: 30179) ' Qt-3 + Qt-Z + Qt-l + E(Qty-0) E(Y79) ' Qt-3 + Qt-Z + Qt-l + Qt-4 51 where: Qt-3 is the accounting data item in the first quarter 1979. Q Q t-2 is the accounting data item in the second quarter 1979. t-l is the accounting data item in the third quarter 1979. Use of the naive model is supported by previous research. Brown and Kennelly (1972) used this model to develop expectations of earnings. Beaver (1974) used a similar naive model which included a drift term in his study of the information content of the magnitude of unexpected earn- ings. Foster (1977) presents evidence that this naive model is a good representation of the underlying market process. He found, using this model, a significant association between the sign of the earnings change and the sign of the cumulative average residual. Market Reactions Other components of the research framework are the measures of market reaction. The measures used are the monthly cumulative abnormal return, for price reactions, and the monthly cumulative abnormal volume, for volume reactions. The cumulative abnormal return, CAR, is expressed as: T CAR - : eit where: - R - (a'+ b Rmt) 8it it t - December 1979 through March 1980 The cumulative abnormal volume is determined similarly: T CAV - 2 u t it where: l‘it - Vit - (c + d Vat) t - December 1979 through March 1980 52 Three steps are required to obtain each of these measures: 1. Develop the estimation equations: fiit - a + b Rmt by regressing individual firm monthly re- turns on the monthly returns of the market for the period January, 1975 through November, 1979. vit - ci+ d th by regressing the monthly percentage of shares traded for an individual firm on the monthly per- centage of shares traded for the market for the period January, 1975 through November, 1979. 2. Apply the return and volume estimation equations to estimate the expected returns and volumes for December, 1979 through March, 1980. 3. Sum the residuals from both the returns and the volume esti- mates to obtain the cumulative abnormal return, CAR, and the cumulative abnormal volume, CAV. Data Summary The previous research steps are required to obtain the data to be used for parameter estimation and model testing. An analysis of the data indicated that nine firms needed to be eliminated due to structural changes in the firms. These structural changes involved events such as an increase in debt or mergers with other firms during the test period. The expectation errors associated with these firms were many standard deviations away from the mean and biased both the mean and variance- covariance estimates. Table 6 provides a summary of the data after the outliers were eliminated. Table 7 is the lower left triangle of the cor- relation matrix for the variables used in this analysis. Table 6. Variable 13 Summary of Data Description CAR GAY expectation error re- garding the current ratio expectation error re- garding the quick ratio expectation error re- garding the defensive interval expectation error re- garding the debt equity ratio expectation error re- garding the long term debt to equity ratio expectation error re- garding times interest earned expectation error re- garding rate of return on SSSECB expectation error re- garding the earnings to sales ratio expectation error re- garding the primary earnings per share expectation error re- garding the rate of return on common equity expectation error re- garding the asset turnover ratio expectation error re- garding the accounts receivable turnover ratio expectation error re- garding the inventory turnover ratio 53 Mean Standard Deviation Minimum Maximum .013999 .011108 .001999 -2.1386 -.002666 .001612 -1.1661 .004051 .000210 -.002815 .011448 .049945 .34298 .18559 .16773 .12613 .29308 .20836 17.734 .038727 .033998 7.0938 .017241 .010824 .94573 .07522 .14935 1.6558 1.0347 -.63275 -1.0674 -.93942 -52.496 -.11079 -57.936 -.072613 -.048682 -3.0700 -.66535 -.74842 -8.1015 -4.5998 .65240 .61413 1.0583 .88883 96.588 .13996 .16910 38.379 .097162 .042475 3.32000 .32500 .69866 7.3380 3.8010 54 coo.H as“. who. o«o.a eeo. onH.I owe. anc.l cqc. noo.l Hw~.u cow. sac. Noe. eeo.: oco.H nan. oofi. sea. cod. can. moc.| Nec. acH.| oa~.| omo.l «no. Hmc.l Hmo.| ooc.a cac. «ac. nmc.c HRH. coo. meo. «wo.u Aeo.l Acc.| coo. $00.: uhc.u ooo.~ mam. wee. Han. mac. .nno.| «HH.I N¢¢.| aoo.a nmo.l Hoo.l coo.| ooo.n has. awn. nna. «~N.t moo.l moc.| «Mo.u «mo.u com. nmn. oco.H was. moo. nNH.I h-.n ace. Hc~.I n¢~.t odd. nan. . ooo.~ nan. ~o~.: ~c~.: nso.l nmo.n cco.l Hoe. one. ace.“ 506.: ssc.l awe. coo. HoH. uma. nwo. oco.~ nee. moo. nHm. can. ono.l Heo.u coo.H «an. HwH.I nun.| «no. oHH. ooo.~ nnu. nqo. «ca. “ma. ooo.~ «on. Hmo.| mno.u oco.H oHH.I mNH.n occ.~ mow. ooc.~ man «an Hex aux , ax on an on an «x mm «x as N» as hwu>auo< muuaueeuuuoum oueuo>oa wwaousoua III assuuuoom nexus: ma NH Ha OH mumzamc< mo moaomwum> may no xenon: :oHuoHouuou one we odwcmwue smog nosed .m wanes 55 Confirmatory Analysis of Hypothesized MOdel The hypothesized model (Figure 8) depicts a measurement model where there are four underlying financial dimensions. The expectation errors regarding these four dimensions are measured by the expectation errors regarding the common ratios for that dimension. This model hypothesizes that the expectation errors regarding the financial dimensions are caus- ally linked to the market reactions. The specifications for this model are the following: The prediction model: n1 ' Yll 51 + Y12 g2 + Y13 63 + Y14 54 + 51 n2 ‘ Y21 E1 + Y22 E32 + Y23 63 + Y24 54 ‘ 821 n1 + C2 and the measurement model: x1 ' A11 5:1 + 51 x8 ' A32 53 + 68 x2 ' A12 E1 + 62 x9 ' A33 53 + 59 x3 ' x13 F’1 + 53 3 x10 ' A34 53 + 610 x4 ' A21 52 + 54 x11 ' A41 54 + 511 x5 ' A22 62 + 65 x12 ' X42 54 + 512 x6 ' A23 62 + 66 x13 ' A43 54 + 513 x - A + 6 7 31 E3 7 Appendix D contains the parameter specifications of this model. The Full Information Maximum.Likelihood (FIML) estimates, their standard errors, and the corresponding T-values for the parameters of the hypothesized model are presented in Table 8. 56 61 Z; XI \ 62 % x2 e £1 63 4 x3 / éu —=¢ *4 e\\\\\\\\\\\ 55 ”7* x5" £2 n 66 1* x6 57 % x7 68 if X8 4WL 69 e 510 f 631 2‘ X11\ 612 —e X12:>———————— 513 i "13/ Figure 8. Hypothesized Causal Model “‘ Ll Table 8. Estimates of Parameters for Hypothesized Model 57 Parameter Number 10 11 12 13 14 15 16 17 18 19 20 21 22 23 (A11) (A12) (A13) (A24) (1 (A 25) 26) (A37) (A38) (A39) (*3 1o) (*4 11) (*4 12) (‘4 13) (821) (Yll) (le) (Y13) (Y14) (Y21) (Yzz) (Y23) (Y24) (o 5152 ) Estimate 1.007 .838 .038 .072 9.362 -.003 1.051 .755 .540 .550 .806 .413 .569 -.392 -.114 -.008 .143 -.122 -.056 -.001 -.006 -.034 .057 Standard Error .059 .063 .070 .597 76.653 .026 .054 .062 .065 .065 .099 .083 .087 .066 .071 .071 .070 .088 .066 .012 .065 .082 .470 T-Value 17.146 13.349 .545 .121 .122 -.117 ‘19.493 12.106 8.268 8.431 8.129 4.981 6.519 -5.917 -l.611 -.120 2.034 -1.385 -.850 -.108 -.O96 -.415 .121 58 Table 8. (cont'd) Parameter Number Estimate Standard Error T-Value 24 (o ) -.007 .066 -.112 a a 1 3 25 (o ) .010 .087 .121 a 5 2 3 26 (o ) .122 .082 1.483 a a 1 4 27 (o ) .016 .131 .121 a a 2 4 28 (o ) .289 .075 3.851 5 E 3 4 29 (62:1) .958 .096 9.938 30 (62:1) .834 .084 9.970 31 (0251) -.015 .063 -.236 32 (0252) .298 .053 5.647 33 (0253) .999 .100 9.975 34 (0254) .997 .132 7.573 35 (0255) -86.366 1435.368 -.060 36 (0256) 1.000 .100 9.975 37 (0267) -.104 .055 -1.897 38 (0258) .430 .050 8.546 39 (0269) .708 .071 10.005 40 (025 ) .697 .070 9.985 10 41 (02511) .351 .134 2.621 42 (02512) .830 .092 9.017 43 (02513) .677 .095 7.135 59 The overall test of model fit, )(2 - 443.3769 with 77 degrees of freedom, implies a poor fit. However, Bentler and Bonett (1980) point out that the overall chi-square goodness of fit test for comparing a hypothesized model against a general alternative model is insufficient when sample size or degrees of freedom are large. They propose the use of a general null model to provide a reference point for the evaluation of covariance structure models. A null model is a severely restricted model that specifies independence among the variables. For the hypothesized causal structure, the null measurement model specifies no common factors by set- ting all factor loadings equal to zero. A - 0 fl The null prediction model specifies no link between the market reaction measures and does not link any of the expectation errors regarding the financial dimensions to the market reactions. 1 0 0 1 £- 1-0 The x? for the null model is 1312.9024 with 105 degrees of freedom. Let C represent the hypothesized causal model and Co the null model. 1 The test of model equivalence, a test of the equality of parameters for the two configurations, can be made. Let Ho represent the null hypothesis of model equivalence. Ho: Co - C1 This can be tested since the difference between the observed x 2 values for the models is asymptotically distributed as a chi-square, with de- grees of freedom equal to the difference in the number of parameters 60 estimated for the two models. x2 for Co is 1312.9024 with 105 degrees of freedom x2 for c is 443.3769 with 77 degrees of freedom 1 The X2 variate for the test of model equivalence is: 1312.9024 - 443.3769 - 869.5255 degrees of freedom: lOS - 77 - 28 The hypothesis of model equivalence is rejected at the a - .001 level. This implies that the hypothesized model, C better represents 1. the true causal configuration than the null model, Co.. An index of the amount of information gained in the comparison of the hypothesized model with the null provides additional information about the usefulness of competing models (Bentler and Bonett, 1980, p. 599). The non-normed fit index, sz x2 '” 7&2 " C0 C1 C0 9 - .- 1 c 0 DP DF up 0 1 c0 c1 00 represents the increment in fit obtained by using the hypothesized model structure rather than the null model structure. 1312.9024 443.3769 1312.9024 DC C - -———-—————--——-————- + -——-——-——-- 1 0 1 105 77 105 12.5038 - 5.7581 0 - = .59 C001 11.5038 The normed fit index is given by: 61 since X2 - -2 logarithm of the likelihood ratio - NF where N - sample size and F is the maximum fit 1312.9024 443.3769 1312.9024 ACC -—————-—-—-—— :————- 0 1 200 200 200 6.5645 - 2.2167 A - - .66 C0C1 6.5645 The hypothesized model is a significant improvement over the null measurement model. This causal configuration recreates 66 per cent of the generalized variance of the observed variance-covariance matrix. This implies that 34 per cent of the generalized variance is not explained by the hypothesized model. The parameter estimates and t-values provided in Table 8 indicate that some aspects of the measurement model are inadequate. The expecta- tion error regarding the defensive interval is not a good indicator of the expectation error regarding the liquidity dimension. The expectation error regarding the leverage dimension was not found to be adequately measured by any of the hypothesized indicators. The remainder of the measurement model is quite adequate. The only significant coefficients of the preduction model are 821 and Y13. Abnormal returns are driven by the expectation errors regarding profitability and the abnormal volume is driven by the abnormal returns. 62 The inadequacy of the hypothesized model may be found in the measure- ment model, the prediction model, or both. Bentler and Bonett (1980, p. 604) state, "There may be little point to evaluating a given regres- sion structure if the measurement model is totally inadequate." In order to assess the causal model deficiencies which resulted in such a poor fit, an analysis of the measurement model is undertaken. The hypothesized measurement model is: "1 ' 111 151 + 61 "8 ' A32 E3 + 58 "2'A12 E1"‘52 "9'A33 F’3“59 x3 ‘ 113 51 + 53 A "10 " A34 53 + 610 "4 ' X21 832 + 54 - "11 '° A41 E4 + 511 x5 ‘ A22 52 + ‘55 x12 ' ‘42 E4 + 512 "6 " A23 E32 + 56 4 "13 " A43 E4 + 513 x . 1 + a 7 3153 7 Figure 9. is a diagram of the hypothesized measurement model. The parameter specifications for each of the matrices of this model are pre- sented in Appendix E. Estimation of these parameters produced the parameter estimates, standard errors, and t-values in Table 9. The overall test of goodness of fit, )(2 - 419.2233 with 59 degrees of freedom, indicates the hypothesized measurement model is a poor representation of the structure underlying the observed relationships among the observed exogenous variables, the It's. Let M1 represent the hypothesized measurement configuration and M0 the null measurement model. The test of model equivalence, a test of Figure 9. 63 4 x1 51 413 4* XS £2 _AX7 4"! h‘ \\// \/ v 0 x10 J —e X}2: £4 Hypothesized \ Measurement Model 64 Table 9. Estimates of Parameters for the Hypothesized Measurement Model Parameter Number Estimate Standard Error T-Value 1 (All) 1.015 .059 17.083 2 (112) .864 .063 13.799 3 (113) .102 .070 1.453 4 (124) .154 .253 .605 5 (125) 4.463 7.092 .629 6 (126) -.013 .026 -.505 7 (137) 1.079 .054 19.959 8 (A38) .731 .063 11.693 9 (139) .515 .065 7.914 10 (13 10) .527 .065 8.062 11 (14 11) .807 .102 7.897 12 (14 12) .397 .083 4.785 13 (34 13) .579 .089 6.493 14 (o ) .133 .222 .599 5 E 1 2 15 (o ) .039 .064 .599 5 5 1 3 16 (o ) .034 .059 .583 a a 2 3 17 (o ) .154 .084 1.842 a 5 1 4 18 (o ) .038 .066 .577 5 E 2 4 19 (o ) .275 .073 3.752 E 5 3 4 20 (0261) .017 .059 .292 21 (0252) .284 .052 5.501 22 (0263) .953 .096 9.973 23 (0264) .937 .120 7.822 24 (0255) -18.517 63.364 -.292 25 (0256) 1.043 .105 9.976 65 Table 9. (cont'd.) Parameter Number Estimate Standard Error 21933. 26 (0267) -.159 ' .063 -2.527 27 (0258) .451 .052 8.693 28 (0259) .738 - .073 10.107 29 (02510) .732 .073 10.090 30 (02611) .365 .140 2.616 31 (02512) .835 .092 9.085 32 (02513) .668 .098 6.842 66 the equality of parameters for the two models, can be made. The )(2 for the null measurement model is 1234.3698 with 78 degrees of freedom. Let HO represent the null hypothesis of model equivalence. H0: ME - Mi The ‘x2 variate for the test of model equivalence is: 1234.3698 - 419.2233 - 815.1465 degrees of freedom: 78 - 59 - 19 The hypothesis of model equivalence is rejected at the - .001 level. This implies that the hypothesized model better represents the causal configuration than the null measurement model. The non-normed fit index, 7x2 x2 1 X2 .1 "M M1 DEM DFMI ' DFM O O A L d L - represents the increment in fit obtained by using the hypothesized meas- urement model structure rather than the null measurement model structure. _ fligggggggg, _ 419.2233 ., 1234.3698 _ 1 78 59 78 p ”.“1 . _ 15.8252 - 7.1054 - 911 M ' 14.8252 '53817 The normed fit index is given by: X2 X2 1 X2 Mo _ Ml % Mo AM'N NJN O 67 since X2 - -2 logarithm of the likelihood ratio - NF where N - sample size and F is the maximum.fit _ 1234.3698 _ 419.2233 , 1234.3698]_ 66037 Auoul 200 200 200 ' The hypothesized measurenent model is a substantial improvement over the null measurement model. However, the remaining improvement, 1 - .41183 and l - A - .33963, indicate a more adequate model ' ”H.511 Mo". may be obtained. This implies that the hypothesized measurement model is inadequate from both a statistical and a practical point of view. ExploratoryiAnalysis of Measurement Models Given the inadequacy of the hypothesized measurement model an ex- ploratory analysis was undertaken to identify a valid measurement model. To accomplish this the squared correlation matrix was computed and the x variables were aggregated according to concomitant variation. Variables with a high degree of covariation are presumed to be indicators of a common underlying dimension. The squared correlation matrix and the seven identified factors are presented in Table 10. This new'measurement model, M2, has seven underlying dimensions. The expectation error for the liquidity dimension is represented by the expectation errors for the current ratio and the quick ratio. The expec- tation errors regarding the defensive interval, the long term debt to equity ratio, the total debt to equity ratio, and the times interest earned ratio are indicators of themselves. The expectation errors for the ratios measuring profitability and activity remain the same as the hypothesized measurement model. The dimensions are allowed to covary but no indicator is allowed to measure more than one dimension. Figure 10 is a diagram of the measurement model M2. The parameter specifications for the exploratory measurement model M Table 11. presents the estimates, standard errors, and t-values for the parameters estimated for M2. 68 2 are provided in Appendix F. Table 10. Squared Correlation Matrix for x Variables x Variable 7 8 9 10 4 5 2 1 6 3 11 13 12 100 93 88 86 ~41 ~30 -18 ~10 35 -18 26 9 49 8 93 100 83 81 ~26 ~35 ~31 ~26 26 3 ~3 ~19 28 88 83 100 70 ~34 -38 ~14 ~10 31 ~9 18 7 37 10 86 81 70 100 ~29 ~22 ~19 ~13 23 ~13 18 ~2 34 4 ~41 ~26 ~34 ~29- 55 ~22 ~36 ~20 30 ~26 ~19 ~27 5 ~30 ~35 ~38 ~22 55- 50 45 -6 11 6 13 ~3 2 ~18 ~31 ~14 ~19 22 50 100 96 12 27 0 29 ~12 1 ~10 ~26 ~10 ~13 ~36 45 96 100 17 9 13 27 4 6 35 26- 31 23 ~20 -6 12 17- 13 ~1 ~11 4 3 ~18 3 ~9 ~13 30 11 27 9 13 100 ~87 ~46 ~51 11 26 ~3 18 18 ~26 6 0 13 ~1 -87 100 74 6O 13 9 ~19 7 ~2 ~19 13 29 27 ~11 -46 74 100 40 12 49 28 37 34 ~27 ~3 ~12 4 4 ~51 6O 40 100 511 512 Figure 10. Exploratory .xl, 69 x31 52 x“; (2., x5 1, 5“ X6 ¢~ £5 "7 "9 x10 /\\ ”121’ 57 \ x13 Measurement Model M2 70 Table 11. Parameter Estimates for Exploratory Measurement Model M 2 Parameter Number Estimate Standard Error T-Value 1 (All) .951 .056 16.835 2 (112) .888 .059 15.165 3 (167) 1.047 .053 19.715 4 (A68) .757 .062 12.241 5 (A69) .547 .065 8.406 6 (16 10) .552 .065 8.490 7 (A7 11) 1.115 .083 13.478 8 (A7 12) .268 .066 4.054 9 (17 13) .437 .071 6.131 10 (o ) .114 .073 1.562 E E l 2 11 (o - ) -.301 .072 -4.197 E1"3 12 (o; , ) .222 .073 3.057 1293 13 (or - ) .337 .071 4.725 Vlgé 14 (c ) .008 .071 .113 E E 2 4 15 (CE , ) .465 .078 5.948 3’4 16 (0E r ) .095 .073 1.299 1’5 17 (o ) .089 .071 1.250 5255 18 (o , ) —.O77 .071 -l.083 £395 19 (o ) -.007 .071 -.099 £455 20 (o E ) -.025 .069 -.365 €1’6 21 (o ) -.100 .067 -1.494 6‘256 22 (o - ) - 246 .067 -3.691 £346 23 (0. ) -.O75 .067 -l.118 24 (o E ) .216 .057 3.237 71 .Table 11. (cont'd.) Eiqwilflbgr 3351111th Standard Error T-V:11_u_e_2_ 25 (sE E ) .049 .065 .754 1 7 26 (or a ) ~.598 .073 ~8.173 ”2 7 27 (65 g ) ~.066 .063 ~1.050 3 7 28 (a5 a ) .039 .063 .620 4 7 29 (aE a ) .015 .063 .240 5 7 30 (65 E ) .161 .059 2.729 6 7 31 (0251) .096 .041 2.346 32 (0252) .212 .041 5.221 9 33 (6'83) 0 .100 0 2 34 (o 64) O . 100 0 2 35 (o 05) 0 .100 0 2 ,, c 36 (o 06) O . 100 0 37 (0257) -.O96 .050 -1.918 38 (0268) .427 .049 8.736 39 (0259) .701 .070 10.029 40 (62810) .696 .069 10.021 41 (02611) ~.243 .159 ~1.533 42 (02512) .928 .092 10.055 43 (32513) .809 .084 9.674 72 The test for goodness of fit, x 2 - 204.1125 with 48 degrees of freedom, implies that M2 does not completely fit the data. Let: M6 be the null measurement model M1 is the priori hypothesized measurement model M2 is the seven factor exploratory measurement model The test of model equivalence, M1 - M2, is: X2 - 419.2233 - 204.1125 - 215.1108 DF - 59 - 48 - 11 The null hypothesis of model equivalence is rejected at a - .001 level. The incremental fit indices of M2 to M0 are: 15.8252 - 4.2523 ”M0112 14.8252 ' 7806 Ann 0 2 1234.3698 204.1125 3 [ 200 - 766...] 6.1718 3 .8346 The incremental fit indices of M2 to M1 are: 7.1054 - 4.2523 9 I Mle 14.8252 .1924 19.2233 204.1125 4 . AMle -[-—-§66— - T] '3' 6.1718 3 .1742 These results indicate that the seven factor exploratory model is a bet- ter model than the hypothesized measurement model. However, a more ade- quate representation seems feasible. An analysis of the observed correlation matrix and iterative model building produced the following measurement model. Attempts to specify 73 additional factors resulted in either insignificant factor loadings or under-identification of the model. This exploratory measurement model consists of seven factors or dimensions in which indicators load on more than one dimension. This exploratory measurement model, M , is: 1 ‘11 a1 + ‘71 g7 + 51 x2 ' ‘12 E1 + ‘22 52 + ‘ E36 + ‘72 57 + 5 + 6 x ' ‘ ‘51 + ‘ 52 + ‘63 E6 3 3 13 X IA 4 34 E3 4 x5 ‘ ‘45 E4 + ‘ g6 + 5 x6 ' ‘56 55 + 6 x I), 7 67 E6 77 x8 ' ‘18 51 + ‘28 52 + ‘68 56 + ‘78 57 + 58 x9 ' ‘69 56 + ‘79 57 + 69 x10 ' ‘6 10 E36 + 610 x11 3 ‘6 11 a6 + ‘7 11 57 + 511 x12 ' ‘1 12 51 + ‘6 12 a6 + ‘7 12 E7 + 512 x13 ‘ ‘1 13 51 + ‘7 13 a7 + 513 where: A = A = A = A a A = A a A = 1.0 12 23 34 45 56 67 7 11 Figure 11. is a diagram representation of the exploratory measurement model M3. 74 61 A 62 g; 63 Av 64 ‘J‘ 55 A: 58 67 A 63 .3 69 4—9 510 511 A? 512 4' x13 ‘13 l S be to ed train cons are ome nd 5 d to covary a llowe re a rs a facto the of (Some -) orthogonal nt Model M3 e tory Measurem lora Exp 11. Figure 75 The x2 test of goodness of fit is 91.3119 with 40 degrees of freedom. Let M3 be the seven factor, multiple loadings exploratory measure- ment model. The test of equivalence between the seven factor model M2 and the seven factor multiple loadings model M3 is: Ho: M2 - M3 x2 - 204.1125 - 91.3119 - 112.8006 DF - 48 - 4O - 8 no is rejected at the c - .001 level. The incremental fit indices are: . 1234. 3698 _ 91.3119 . 1234.3698 _ 1 - 91 0M M 40 ' 78 ' o 3 r- 1' 1234. 3698 91.3119 1234.3698 _ AM M ' 200 ' 200 * 200 '93 o 3 L ._ _ 7 1054 ~ 2.2827 . 33 14.8252 ' . 4.2523 - 2.2827 3 M3 [ 14.8252 ] '13 _ 2.0961 ~ .4566 . 27 M3 6.1717 ° _ 1.0205 ~ .4566 3 09 AM2M3 6.1718 ' These indices indicate that M is a better representation than either M1 3 or M2. However, the inability to interpret this model makes it much less desirable than M?- 76 Exploratory Analysis of Prediction Models In order to evaluate the prediction or structural model, an explor- atory analysis based on the measurement models previously discussed is conducted. The measurement models, M2 and M3 of the previous section are taken as given and the structural parameters are estimated and the pre- diction model evaluated. Exploratory Analysis of Prediction Models Based on the Measurement Model M2 The measurement model M2 is a seven factor nonmultiple loading model where the factors are allowed to covary. Given this measurement model the prediction model is investigated. The first model investigated links all seven of the dimensions to each of the market reactions and does not link the market reactions directly. This exploratory prediction model, P1, is depicted in Figure 12. It causally links the expectation errors for the seven dimensions of M2 to the market reaction measures. It is presumed that all causal factors have been included and the prediction errors are not allowed to covary. The parameter specification for the prediction model are provided in Appendix G. The estimates, standard errors, and t-values for the structural parameters are provided in Table 12. 511 5:: Figure 77 .,,\.c 13% L2 -“(1 \ x5 < in A‘iilL. x‘:$- —“‘S “" t2 Exploratory Prediction Model P1 78 Table 12. Parameter Estimates for Prediction Model P 1 Parameter Number Estimate Standard Error T-Value 10 (711) . -.024 .111 -.218 11 (712) .116 .097 1.186 12 (713) .184 .128 1.431 14 (715) -.002 .071 -.022 15 (716) .157 .072 2.176 18 (722) .077 .095 .813 19 (723) .099 .120 .827 20 (724) -.073 .111 -.660 21 (725) .128 .073 1.757 22 (726) ' .025 .072 .345 45 (02(1) .933 .094 9.977 46 (oztz) .956 .096 9.967 79 The x2 goodness of fit is 253.4780 with sixty-one degrees of freedom. Respecification of the exploratory prediction model P1 to in- clude a causal link between the volume and price reactions is undertaken. This exploratory prediction model, P2, is depicted in Figure 13. The parameter specifications are provided in Appendix H. Table 13 provides the parameter estimates, standard errors, and t-values for the exploratory prediction model P2. 80 6’ —: K, \ (.2 4 '2 63 : :3 :f (.2 6.. a “1.:— (3 1,1... ~u 55 # "5 3 £4 “ 66 4. x64— "(5 x 67 ‘ x7 1‘:E"\\‘ 5 5 5: wt" I / £6 5, i- 359 / 6", fi‘ “)0 5” z x”\ 612 : x12:ardrwrtar””£7 6” 4. "13 Figure 13. Exploratory Prediction MOdel P2 81 Table 13. Parameter Estimates for Prediction Mbdel P2 Parameter Number Estimate Standard Error T-Value 10 (821) -.387 .066 ~5.842 11 (711) -.028 .107 ~.265 12 (712) ' .116 .095 1.230 13 (713) .175 .120 1.455 14 (114) ~.132 .110 -l.l98 15 (715) ~.001 .071 ~.019 16 (116) .154 .071 2.175 17 (717) ~.003 .074 ~.037 18 (721) ~.058 .095 -.610 19 (722) .033 .085 .391 20 (y23) .025 .102 .248 21 (724) ~.016 .096 ~.172 22 (725) .128 .068 1.897 23 (726) ~.o34 .065 ~.514 24 (727) ~.007 .067 ~.100 46 (62:1) .935 .094 9.992 47 (62:2) .817 .082 9.972 82 The x2 value associated with this model is 222.0590 with 60 degrees of freedom. The test of equivalence between these two prediction models based on .P2 x2 - 253.4780 ~ 222.0590 - 31.419 DF I 61 - 60 - 1 The hypothesis of model equivalence, H0, is rejected at the (x- .001 level. The incremental fit indices due to the structural parameter re- lating CAR to CAV are: 9P P W[[253 4780]_ [222.0 0590 ‘* 276%3264 _ i . .1692 1 2 3‘ L 253. 4780 222. 0590 , 276.3264 ' A111172”l:"""""'200 ]" [*— 200 ]: L 200 ] '1‘37 Given this incremental fit and the t-value of -5.842 for 821 it is apparent that this causal link is quite important. In order to explore the respecification of the prediction model an analysis of the degree of multicollinearity is necessary. The correla- tions among the estimates for the parameters of the P prediction model 2 are provided in Table 14. Collinearity is present and it is expected since the measurement model employed is oblique. A comparison of the highly correlated estimates with the correlations among the variables up- holds the observed collinearity. The effect of the multicollinearity is to make interpretation of the individual coefficients difficult. Causal paths of correlated variables will be deleted by only allowing one path to exist for a pair of correlated variables. Exploratory analysis of other prediction models will incorporate this specification. 83 oo.~ o-.- ooo.- and. non.. ”an. m-.- moo. nooo- ~oo.- ooo. noo.- too. o~o.- ooo. oo.« oo~.- ano.- now. nmo.u moo. noo.u ~oo.- goo. hoo.- ooo. noo.- moo. one. ow» oo.~ oHo. moo. oo~.u Noo.- ~oo.- Noo. ooo. Hoo.- goo. ~oo.- goo. moo. «N» oo.H ooo.- "on. ano.- «so. ooo.- ooo.a “No. -o.u too. ooo.u hoo.u om» oo.~ soo.- ooo. ooo.- ,omo. soo. hoo.a Nmo. HNo.u nNo. ooo. MN» oo.H non.- ooo.. ooo.- ~oo.- ooo. ooo.- oNo. ooo.u moo. NN» oo.~ ooo.- ooo. goo. o~o.- oNo. meo.- ooo. o~o.- o~> oo.~ omo.- noo.- moo. ~m~.- ohm. oo~.- ooo. NH» oo.~ no~.n boo.u ”on. ooo.- oNN. ooo. oo» oo.a ooo. «Ho. nos.- ono.- ~oo.- as» oo.« onh.u oon. ooo.u goo. oo» oo.~ ooo.- goo. ooo.- no» oo.~ n~o.u moo. «or oo.~ ooo.-. as» oo.~ oNo -> ow» nN» om» nu» -> H~> as» oar no» so» no» No» as» . “No oN n~ - HN on as o“ as oo no .oa no NH so o“ «m Hobo: oofiuofiooum you xfiuumz cowumaouuoo mouwsqumm nouoaouom mo mamoowue uwog nose; .oH ofiooe 84 Through iterative building of a prediction model using the M2 measurement model an optimal prediction model was found. The optimal configuration provided the lowest )(2 value given the degrees of freedom. In this prediction model the price reaction is driven by the expectation errors regarding the profitability dimension, the total debt to equity ratio, and the long term debt to equity ratio. The volume reaction is driven by the price reaction and the expectation error regarding the times interest earned ratio. Figure 14 depicts this exploratory predic- tion model, P3. The parameter specifications for this prediction model are provided in Appendix I and the parameter estimates are provided in Table 15. 0 611 512 Figure 85 ..,,\-£ 1 x2 / x3 1 52 x“:— 4-£3\‘ /"14 "5‘ CI. T x6- "7 ’ A 8‘\ “2 f £6 N 812;— £7 \ “)3 l4. Exploratory Prediction Model P3 {1 ‘2 86 Table 15. Parameter Estimates for Prediction Model P3 Parameter Number Estimate Standard Error T-Value 10 (821) -.399 .064 -6.195 11 (Y13) .233 .088 2.649 12 (Yl4) -.l70 .084 -2.033 13 (Y16)' .156 .068 2.280 14 (725) .116 .065 1.774 36 (ozgl) .945 .095 9.963 37 (62:2) .825 .083 9.974 The X2 value associated with this model is X2 8 226.4839 with 70 degrees of freedom. The test of model equivalence between this prediction model and the null prediction model is: Ho: Po - P3 x2 - 276.3264 - 226.4839 - 49.8425 DF 8 75 - 70 ' 5 The hypothesis of model equivalence is rejected at the a a .001 level. The incremental fit indices comparing this prediction model to the null prediction model are: r o _ 276.3264 _ 226. 74839 #[ 76. 3264 _ 1] _ .1672 PP 75 0 3 A _ [276.3264] _ [226. 4839] - 20 9093 L 200 0 I. 276 .3264] 200 a .1803 87 A test of model equivalence between prediction models P2 and P3 resulted in the failure to reject the null hypothesis of equivalence. The incre- mental fit indices comparing the total models (measurement model M2 and the prediction models, P1, P2 or PB‘Dagainst the total null model are: 1312.9024 253.4780 1312.9024 p a - --——-- 9 ~--—--—--- - 1 = .7257 N0P1 105 61 105 1312.9024 253.4780 1312.9024 A . _________....________ % -————————— = .8069 N0P1 200 200 200 1312.9024 222.0590 1312.9024' p a -—-—-————----—-—-—- 3% -—————-—-— - 1 - .7652 N092 105 60 105 1312.9024 222.0590 1312.9024 A P . -—-———-—+---—-—-——- e- -;-—-—-- - :8309 No 2 200 zoo zoo 1312.9024 226.4839 . 1312.9024 ”N P a :—-——-- - -——--—- % -—-—-———-— - 1 - .8057 o 3 105 70 105 1312.9024 226.4839 1312.9024 AN p ‘ """""""‘--- * ---—-- - .8275 o 3 200 200 200 Exploratory Analysis of Prediction Mbdels Based on the Measurement Model M3 The measurement model M3 is a seven factor oblique model in which the indicators load on multiple factors. Through iterative modelling a model with the lowest 2 value relative to the number of degrees of freedom.was constructed. Since this prediction model is based on the un- interpretable measurement model M: a description of the model is not possible. Figure 15 is a diagram of the model. The parameter specifi— cations for the prediction model P4 are provided in Appendix J. 88 Figure 15. Exploratory Prediction Model P4 89 The parameter estimates, standard errors, and t-values are presented in Table 16. Table 16. Parameter Estimates for Prediction Model P 4 Parameter Number Estimate Standard Error T-Value 17 (821) -.397 .065 -6.092 18 (yll) -.010 .036 —.275 19 (712) .151 .092 1.649 20 (713) .119 .078 1.537 21 (716) .039 .100 .389 22 (721) -.005 .032 ~.147 23 (yzz) .055 .082 .667 24 (725) .123 .067 1.836 25 (726) -.067 .088 -.770 47 (62:1) .955 .095 10.012 48 (62:2) .823 .082 9.979 This model has a x2 value of 114.3288 with 59 degrees of freedom. The test of equivalence between this prediction model and the null pre- diction model is rejected at the a - .001 level. no: Poo - P4 x 2 - 163.5489 - 114.3288 - 49.2201 DF - 68 - 59 - 49.220 The associated incremental fit indices are: up P - .3326 AP P - .3009 90 The incremental fit indices between the total null model and this total model (measurement model M3 and prediction model P4) are: 1312.9024 114.3288 1312.9024 . -—————-——— - -——-————— % ————-—-——- - 1 = .9185 p N0P4 105 59 105 1312.9024 114.3288 1312.9024 AN P = -—-——————---——-———- 8 -————————- s .9129 0 4 200 200 200 Interpretation of Exploratory Analysis of Prediction Models The exploratory analysis of prediction models P2, P3 and P4 indicates a very significant causal link between abnormal volume and abnormal re- turns. Also a strong link between the expectation errors regarding pro- fitability and abnormal returns is evident. The prediction model P3 re- sults indicate the usefulness of the long term debt to equity ratio, the debt to.equity ratio, and profitability data. The failure of P4 to find any significant causal paths other than 321 is not a surprise. The underlying measurement model employed allows the expectation errors to load on multiple financial dimensions. Although this provides a better measurement model, the interpretation of the meas- urement model is difficult and the usefulness of the implied factors is negligible in the market. Even though the measurement model M3 is a better fit the prediction model implies that the market does not find the measurement model to be useful. Analysis AsauminggPixed X Since the fit of a structural model depends on the measurement model employed, a poor measurement model produces a poor fit of the total model and makes interpretation of the structural coefficients very difficult. 91 The inability to find an adequate measurement model configuration is not surprizing given the results of the Stevens (1973) and Johnson (1979) studies presented in Chapter II. One expects to encounter some difficulty in developing a measurement model if the indicators load on multiple fac- tors. Another mode of analysis, often employed in econometrics, which ignores the problem of an inadequate measurement model is to treat the x variables as fixed. This means that each x is treated as a single measure of a particular 5. The coefficient relating x to E, A, is fixed at 1.00 and no measurement error exists. A = I and 0 = 0 -x - 6 -— The total model consists only of a structural or prediction model, £1'£§.+5_ since there is no measurement model. For this study, treating x as fixed implies that the expectation errors regarding the financial ratios are not multiple indicators of the expectation errors for the four underlying financial dimensions. Instead each expectation error regarding a ratio is treated as the expectation error regarding a unique attribute of the firm. A number of models were developed, estimated, and tested. Fourteen of these models are presented. Fixed X - Model 1 is a saturated causal model where the market reactions are driven by all of the expectation errors regarding the ratios. Figure 16 is a diagram.of this model. Figure 17 is a diagram of the Fixed X - Model 2. This model has the price reaction driven by the volume reaction and the expectation errors regarding the defensive interval, the debt to equity ratio, the rate of return on assets, the earnings to sales ratio, primary earnings per share, 92 and the rate of return on common equity. The prediction errors are also allowed to covary. The Fixed X - Model 3 configuration has the market reactions driven by the expectation errors of the ratios for liquidity, leverage, and pro- fitability. The volume reaction is linked to the price reaction. Figure 18 represents a diagram of this configuration. Figure 19, a diagram of the Fixed X - Model 4 configuration, has the price reaction driven by the expectation errors regarding the defensive interval, the total debt to equity ratio, the rate of return on assets, the earnings to sales ratio, primary earnings per share, and the rate of return on common equity. The volume reaction is causally linked to the expectation errors for the times interest earned ratio, the rate of return on assets, and primary earnings per share. The Fixed X - model 5 configuration adds a causal link where the volume reaction is driven by the price reaction to the Fixed X - Model 5 configuration. This model is presented in Figure 20. N M M m H ID Q \l m H N ("I H ('1 m ("I m I"! ('1 0" In t u N o-I Figure 17. £1 £2 " 0 £8 £9 db £10 £11 £12 £13 Fixed X - MOdel 2 C1 C2 9S "F 4 .. \\\ E7 ..y“ ‘0 \ E8 _ ' 1 Figure 18. Fixed X - Model 3 Cl ‘12 Figure 19. £1 £2 53 £10 £11 £12 £13 d X - Model 4 Fixe Cz Figure 20. 97 E1 52 53 £4 01 £5 II £6 " it £8 4'12: £9 £10 £11 £12 £13 Fixed X - Model 5 41 C2 98 The Fixed X - Model 6 causal configuration adds reciprocal causality to the previous model. This model is diagrammed in Figure 21. The next model, Fixed X - Model 7 diagrammed in Figure 22, drops the reciprocal causality of the previous model and has price reactions driving the vol- ume reactions. The Fixed X - Model 8 configuration has the price reaction driven by the expectation errors regarding the defensive interval ratio, the debt to equity ratio, the rate of return on assets, primary earnings per share, the rate of return on common equity, the asset turnover ratio, the ac- counts receivable turnover ratio, and_the.inventory turnover;ratio. The, volume reaction is driven by the price reaction as well as the expecta-_ tion errors concerning the current ratio, the times interest earned ratio, the rate of return on assets, the earnings to sales ratio, primary earn- ings per share, the asset turnover ratio, the accounts receivable turn- over ratio, and the inventory turnover ratio. This model is presented in‘ Figure 23. In Model 9 the volume reaction is driven by the price reaction and the expectation errors for the current ratio, the times interest earned ratio, the rate of return on assets, the earnings to sales ratio, primary earnings per share, and the inventory turnover ratio. The price reaction is driven by the expectation errors concerning the defensive interval, the debt to equity ratio, the rate of return on assets, the rate of re- turn on common equity, and primary earnings per share. The prediction errors covary. This model is presented in Figure 24. The Fixed X - Model 10 configuration deletes the covariation among the prediction errors and allows reciprocal causation among the market reactions. Figure 25 presents this model. The next model, Fixed X - Model 11 eliminates the causal link from the volume reaction to the price reaction of the previous model. Figure 26 represents this model. 99 £1 £2 £3 £4 \ ”1 £5 ll £6 57 O} £8 ~4:02:‘ 59 £10 £11 £12 £13 1 6 Figure 21. Fixed X - Mode E1 ‘2 100 £1 £2 £3 £4 £5 £6 £8 ~: '12? £9 £10 £11 £12 £13 - del 7 e 22 Fixed X Mo Figur . £1 £2 M \l M O (‘1 IO M H O M H on n H N re 23. Fixed X - Figure 24. £1 £2 £3 £4 £5 £6 £7 .. 4r £9 102 ”1‘ £10 £11 £12 £13 Fixed X - Model 9 £1 t2 103 £1 £2 £3 £4 : / g, 9 £8 'x J. ‘9 e: n24 £10 £11 £12 £13 Figure 25. Fixed X - Mbdel 10 C1 C2 104 £1 £2 £3 £4 L 9 ‘° :1 2: £9 £10 £11 £12 £13 del 11 26 Fixed X - Mo Figure . £1 £2 105 The next causal configuration, Fixed X - Model 12, does not have covariance among the prediction errors. The volume reaction is driven by the price reaction and the expectation errors of the times interest earned ratio, the rate of return on total assets, the earnings to sales ratio, primary earnings per share, and the inventory turnover ratio. The price reaction is driven by the expectation errors for the current ratio, the defensive interval, the debt to equity ratio, the rate of return on total assets, primary earnings per share, and the rate of return on common equity. Figure 27 is a diagram of this model. Figure 28 is a diagram of the Fixed X - Model 13 causal configuration. This model has the price reaction driven by the expectation errors for the current ratio, the defensive interval, the debt to equity ratio, the rate of return on total assets, primary earnings per share, and the rate of return on common equity. The volume reaction is dependent on the price reaction and the expectation errors for the current ratio, the times interest earned ratio, the rate of return on assets, the earnings to sales ratio, primary earnings per share, the rate of return on common equity, and the inventory turnover ratio. The next model, Figure 29, is a saturated model in which the market reactions depend on all of the ex— pectation errors and the volume reaction is dependent upon the price re- action. Table 17 presents the t-values associated with the structural coef- ficient estimates for these fourteen models. The x2 value and the degrees of freedom for each model are provided as well as the (>1evel of signif- icance for the overall test of model fit. Also, the proportion of vari- ation in the endogenous variables accounted for in each equation for the various models is given. The P level provides the probability of obtain- ing a. X2 value larger than the value obtained, assuming the hypothesized model holds. Figure 27 . 106 £1 £2 £3 £4 a: - £5 £6 £7 £8 ‘9 \/// 4 n2 1 £9 £10 £11 £12 £13 Fixed X - Model 12 £1 :2 Figure 28. 107 £11 £12 £13 Fixed X - Model 13 £1 £2 108 £1 £2 £3 :\ .5 w. ‘88:. // " 0‘33? £ 8 $5. \\ av? 11 j g "1‘ : n2 1 £9 I, 810 // £11 £12 £13 4 Figure 29. 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Tests of model equivalence indicate that Models 1, 2, and 4 are equivalent, Models 5, 6, and 7 are equivalent, and Models 3, 9, 10, ll, 12, and 13 are equivalent. The hypotheses of model equiva- lence are rejected for other comparisons. Interpretation of the structural coefficients and the significance of causal links of a model are dependent upon the collinearity of the exo- genous variables. Analysis of the matrix of correlations for the coef- ficients of the saturated model (Model 14) indicates some problems. Appendix X contains the lower left triangle of the correlation matrix of the coefficient estimates for Model 14. However, elimination of one variable from each pair of collinear variables is provided in Model 13. The structural coefficients of Model 13 relating the abnormal returns to the expectation errors regarding various financial ratios are presented in Table 18. Table 18. Parameter Estimates for Price Reation Links for Fixed X - Model 13 Standard Cue Coefficient Error T-Value Current Ratio -.105 .072 -l.447 Defensive Interval .129 .070 1.851 Total Debt/Equity Ratio .080 .076 1.048 Return on Assets .105 .100 1.051 Primary Earnings per Share .202 .083 2.430 Rate of Return on Common Equity -.116 .083 -l.398 While indicating that some information cues other than profitability are linked to market price reactions, the most significant coefficient is the link pertaining to primary earnings per share. The sign of this 111 coefficient is as expected. Good news, a positive forecast error, results in a positive abnormal return. For the other coefficients, the signs are meaningless given the magnitudes of the standard errors. The estimates of the structural coefficients linking the market vol- ume reactions to the financial ratio expectation errors for the Fixed X - Model 13 are presented in Table 19.- Table 19. Parameter Estimates for Volume Reaction Links for Fixed X - Model 13 """""""""""""""""""""""""""""""" § EJEEJ£5"'""" Cue Coefficient Error T-Value Current Ratio -.064 .064 - .994 Times Interest Earned .150 .066 2.281 Return on Total Assets -.314 .120 -2.603 Earnings to Sales Ratio .182 .114 1.591 Primary Earnings per Share .247 .078 3.177 The abnormal volume reation is most significantly linked to cues re- garding profitability. Although the times interest earned ratio is clas- sified as a measure of leverage it can be deemed a profitability indicator. The signs of the coefficients linking abnormal volume to the expec- tation errors regarding times interest earned and primary earnings per share are as expected. Good news regarding these items results in in- creased trading. The sign of the coefficient between the expectation error of the return on total assets is negative and is not as expected. This implies that good news is accompanied by a decrease in trading and bad news results in increased trading. Although there is no apparent reason for this relationship, data items involving the balance sheet tend to have negative coefficients. Another reason for the negative coeffi- cient may be that the return on total assets does not specifically relate 112 to a beneficial or detrimental position for the equity holder. The effect on equity of a change in the return on total assets is conditioned upon changes in the debt structure of the firm. Therefore the signal may be ambiguous to the stockholder. The most significant causal link is the coefficient relating abnormal volume reactions to abnormal price reactions. The estimate is -.355 with a standard error of .064. The associated t-value is -5.523 which is sig- nificant at the <1 - .0000002 level. Since the parameter linking CAV to CAR has a negative sign its actual link is positive since the equation formulation for the model includes -821 on the right hand side. Abnormal volume of a positive nature re- sults when positive abnormal returns occur. Given a specific causal model, the association between an exogenous and an endogenous variable can be decomposed into multiple components. The total association or implied slope is the zero-order correlation bee tween the two variables (Alwin and Hauser, 1975, p. 39). This total associatibn is made up of the total causal effect and the noncausal com- ponent. The noncausal component represents association between to vari- ables due to nondmodeled common causes, collinearity among explanatory variables, and any unanalyzed correlation. The total effect indicates the change in an endogenous variable induced by a change in an exogenous variable. Comprising the total effect are the direct effect and the in- direct effect. The direct effect is the associated path coefficient. Indirect effects are the parts of a total effect due to an intervening variable. Table 20 presents the results of an effect analysis based on Model 13. An analysis of the effect analysis indicates that the relationship between Y1 and Y2 is modeled very well. Overall, the level of noncausal 1513 coco.“ «moo. N y «coo.H Hmoe. Ocno. oooo.a. H r onnn. Haoc. oooo.« «cecal tho.r ma x 00. ad cane. nH ammo. nu on~0.. svHo.I an OnNo.I «800. NH NH OnNo.l Neoo. NH oano.l meno.l «A an an ommo.u «who.o an x noao. ONHH. OH N~80.1 cu oo~H.t OH Nqu.I ooan.l ca 1 HHNo.I o«oo.t ca. K nwno.n nauo. moan. oaou. coon. nnNN. o x 5000.1 nnnn. «wen. HnNO. o h x x mhzmzomzcu A<=mamo< nommmm «0 3158“ .88 «Home 114 components is quite sufficient except for two instances. The direct effect of X7 on Y2 is largely overstated in a negative fashion. This seems to be caused by multicollinearity among X7 and X8. The coefficient relationg X10 to Y1 also is overstated and results in a fairly large noncausal component. Empirical Conclusions For the original hypothesized causal configuration, the results in- dicate that only the profitability data is useful to the investor and results in a price reaction. None of the financial dimensions are direc- tly linked to the volume reaction. Instead, it seems to be driven by the abnormal returns. The interpretation of these results must be made in light of the inadequate overall fit of the model. Exploratory analyses of the measurement model provides insight into the poor fit of the model configuration. Numerous measurement models were investigated; an adequate fitting model was found but its configura- tion was not interpretable. Using the measurement models developed through the exploratory analysis various prediction models were construc- ted, estimated, and tested. These results indicate that profitability information is most useful to the market as a whole however leverage data is also significantly linked to abnormal returns. The abnormal volume reaction is driven by the abnormal returns. By treating each ratio as an individual aspect of the firm the prob- lems associated with the measurement model were eliminated. A number of various prediction models were estimated and tested. These results (Table 17) indicate that the abnormal return reaction is driven by the expectation error regarding earnings per share. The abnormal volume re- action was found to be significantly linked to the expectation errors 115 regarding times interest earned, return on total assets, and earnings per share. This indicates that the individual market participants use more information than the market as a whole. Congruent with the other models, the most significant parameter was the causal link between abnormal trad- ing and abnormal returns. The results overwhelmingly provide evidence that abnormal volume reactions are driven by abnormal returns. This upholds the hypothesis that the market does not adjust prices due to individual investors making shifts in their portfolios but individual investors may make shifts in their portfolios due to changes in the price of a security. An analysis of Fixed X - Model 6 (Table 17) indicates that the link going from ab- normal returns to abnormal volume (£321) is significant and the link go- ing from abnormal volume to abnormal returns ( 812) is not significant. The relationship between abnormal volume and abnormal price is a positive link. Positive abnormal returns drive positive abnormal trading whereas negative abnormal returns result in negative abnormal trading. Good news (positive expectation errors) regarding earnings per share re- sults in both positive abnormal returns and positive abnormal trading. This result, based on a four month reaction period, provides additional insight into the relationship between abnormal returns and abnormal trad- ing. Previous research, Beaver (1968), Kiger (1972), and Morse (1981) analyzed returns and volume on an aggregate level. They did not examine the relationships between abnormal returns and abnormal volume for the individual securities studied. CHAPTER VI Summary, Conclusions, and Implications Summary Previous research has determined that accounting information, in particular earnings, is used by investors and possesses information cone tent. Using the abnormal performance research paradigm this project in- vestigated cue usage resulting from the announcement of earnings and the issuance of financial statements. The information cues investigated con- sisted of: current ratio quick ratio defensive interval debt to equity ratio long term debt to equity ratio times interest earned rate of return on total assets earnings to sales ratio primary earnings per share rate of return on stockholder's equity total asset turnover accounts receivable turnover inventory turnover These cues represent four underlying dimensions of a firm. These dimen- sions are liquidity, leverage, profitability, and activity. Simultaneous equations techniques were used to estimate the parameters and test a hypothesized causal configuration developed in Chapter III. 116 117 The hypothesized model consists of two components; a measurement model and a structural model. The measurement model hypothesized that the expectation errors regarding the financial ratios are multiple indi- cators of the expectation errors for the corresponding financial dimen- sions. Presuming each dimension to be useful to the investor, the struc- tural model causally linked each dimension's error to measures of abnormal return and abnormal volume. A test of model fit indicated that the model was not an adequate representation of the underlying process. Further analysis indicated that the measurement model was misspecified. A number of measurement model configurations were investigated but none were found adequate. The meas- urement model was eliminated and each ratio was treated as a specific attribute of the firm. A saturated structural model linking each of the ratios to market reactions was estimated and tested. Further exploratory analysis was con- ducted and a representative model was found. This model had a very high level of fit (p- .9972). Throughout the various causal configurations analyzed the most in? portant cue was the primary earnings per share datum. Other profitability measures as well as measures of liquidity and leverage were found to be significant. This indicates that investors may utilize other data but earnings per share is most important. It is also consistent with the common stock valuation models. The traditional form of valuation is to discount the future earnings stream. For an individual share of stock, the important parameter is earnings per share. Employment of this type of valuation model by the market would suggest that earnings per share data is useful. The results of this study uphold the usefulness of earn- ings per share data. 118 The most important causal link driving a volume reaction is the abnormal price reaction. This link was found to be the most significant parameter in most of the model configurations. Conclusions The conclusions drawn from this study are threefold. The expecta- tion errors of the financial ratios do not seem to be indicators of the expectation errors of the four financial dimensions of a firm. Instead, each ratio seems to represent a unique attribute to the firm. Second, while liquidity, leverage, and profitability information is useful to the investor, the most important financial datum.is the earnings per share figure. The third conclusion is abnormal returns play a very important role in the causal configuration for abnormal volume. In the saturated model, the abnormal return accounted for eleven per cent of the variation in abnormal volume when a saturated model without this link had an r2 of only thirteen per cent. Assuming abnormal trading activity is an indicator of degree of con- census within the market regarding an information event, a very unique relationship is evident. "Good news" regarding earnings per share is accompanied by a positive abnormal return and positive abnormal trading volume. "Bad news" regarding earnings per share results in a negative abnormal return and negative abnormal trading volume. The signs of the price reaction by the market are as expected. However, the accompanying trading activity implies that "bad news" is interpreted with a high de- gree of concensus. "Good news" is not interpreted with a high degree of concensus and abnormal volume indicates this lack of concensus. An asymetric process regarding the interpretation of information is implied by these results. 119 Implications The results of this study have two major implications. In the realm of policy setting this study contributes to the understanding of account- ing as an information system and the interaction of that system with in- vestors. For the most part, profitability information seems to have the most significant use by investors. The primary earnings per share datum was most important. This upholds the emphasis that has been placed on the income statement by policy making boards. There are two plausible explanations regarding why the market fails to use information cues re- garding liquidity, leverage and activity to the same extent as the profit- ability cues. One explanation is that the quality of the accounting in- formation from the balance sheet may be inadequate due to the standard setting emphasis on the income statement. The second possible reason may be that the other cues do not have a stochastic relationship with future cash flows which is necessary for a cue to have any potential use- fulness (See Chapter II . The results of this project also have implications to research on abnormal returns and abnormal volume. When abnormal returns are investi- gated, the use of the earnings per share cue is required. More flexi- bility is allowed for volume studies since profitability cues other than earnings per share are used by investors. An analysis of the standard errors associated with the structural coefficients linking abnormal returns and abnormal volume to the expec- tation errors for primary earnings per share indicates that the standard error is larger for the former. This implies that a more rigorous test of information content or cue usage results from using abnormal returns. However, in instances where the effect of the cue is expected to be weak the use of abnormal volume is advocated. In the fourteen models estimated, 0 120 where x is fixed, the proportion of variation accounted for is always higher for abnormal volume. This indicates that volume is a more sensi— tive measure of market reaction to information events. Investigations of abnormal volume reactions due to the announcement of earnings should include the causal link between abnormal volume and abnormal returns. Given the significant link between abnormal volume and abnormal price the direct effect of a cue on volume could be insignifi- cant but the indirect effect, through the abnormal return and its link to abnormal volume, significant. The results of the effect analysis reported in Chapter V indicate this composition of direct and indirect causal links. This research project has demonstrated that simultaenous exploration of both price and volume reactions is fruitful. Given the relationship between abnormal volume and abnormal returns, a simultaneous approach is warranted. Recommendations for Future Research In studies of one utilization using the abnormal performance index research paradigm one assumes that the expectation models employed are valid representations of the underlying investor process. Failure to find significant evidence of cue utilization may be symptomatic of an invalid expectation model. Therefore, future replication of this study using other expectation models could ascertain the degree to which the results of this study are contingent on the expectation model employed. Other financial variables not included in this study could be ex- plored as well as other dimensions. Improvement of the measurement model is recommended for future research. This project used a four month reaction period which incorporates more noise into the reaction measures. An approach which would eliminate 121 some of the noise would be to shorten the reaction periods around the release of the financial data. APPENDICES Appendix A LISREL terminology Types of Variables n (eta) £ (xi) Y £91253 Data-oriented Si .5 (sigma) Dependent (endogenous) variable: true (i.e., unobserved) Independent (exogenous) variable: true (i.e., unobserved) Indicator of dependent variable (observed) Indicator of independent variable (observed) Measurement error in observed dependent variable Measurement error in observed independent variable Sources of variance in n not included among the 5's Number of true dependent variables Number of true independent variables Number of observed dependent variables Number of observed independent variables Matrices (p+q x p+q), Variance-covariance matrix among the observed independent and dependent variables (or correlation matrix) (p+q x p+q), Model-generated estimates of variances and covariances among observed independent and dependent variables. Basic Parameter Matrices A 1 bd _y ( am 8) Ax (lambda) (p x m), Matrix of regression coefficients (A's) relating true dependent variables to observed dependent variables (q x n), Matrix of regression coefficients (A's) relating true independent variables to observed independent variables 122 123 (m x m), Matrix of regression coefficients interrelating (m x n), Matrix of regression coefficients (Y's) relating true independent variables to true dependent variables; (n x n). Variance-covariance matrix among true independent variables (or correlation matrix) (m x m), Variance-covariance matrix among zeta variables (p x p), Variance-covariance matrix among epsilon variables (or correlation matrix) (q x q), Variance-covariance matrix among delta variables (m x m), Variancedcovariance matrix among true dependent (m x n), Matrix of regression coefficients for reduced 11 (beta) true dependent variables £_(gamma) indicates direct effect 3 (phi) 1 (psi) (or correlation matrix) fie (theta) 06 (theta) (or correlation matrix) Supplementary Parameter Matrices 2 variables 9. form of structural equations-i.e., coefficients which 'relate each true dependent variables to true independent variables, giving direct and indirect effects combined Appendix B X2 test in the analysis of covariance structures (Bentler and Bonett, 1980) Let Mk be a more restrictive model than Mt' In general, the func- tion L (0) is related to the logarithm of the likelihood function of the observations via L* (O) - -n L (0)/2 + c where c is independent of 0. (See Joreskog: Psychometrica, 1967, 32, 443-482). Let L* (0k) be the maximum of L* (0) under Mk; let L* (at) be the maximum of L* (0) under Mt' Thus * * L (0k) _<_L (0t) since the maximum under a space of restricted range cannot exceed the maximum under a space of less restricted range. Consequently, I * — * log 1 L (0k) L (at) is negative, with 0 < A :_1. To test the null hypothesis of model equivalence (H6: 0k = 0t), (-2 log A) is asymptotically distributed as a chi square variate. The degrees of freedom is the difference in the number of parameters estimated under Mt and Mk' This test is a test of the equality of the parameters under the two models. Since the free parameters in 0 are k a subset of the free parameters in at, various applications of the test can be constructed. The null hypothesis associated with model comparisons has an alternative form. The alternative is that the covariance matrices 124 125 generated by the parameter vectors are equivalent under the Mk and Mt structural models. The significance test is the same as previouSly described. Appendix C Sample Firms ACF Industries Alaska Interstate Alpha Portland Allen Group Amax Amerada Hess American Cyanamid American District Telephone American Water Works AMETEX AMF Ampco Pittsburgh Armada Corp. Asarco Avon Ball Corp Baxnes Group Becker Industries Bell & Howell Bemis B.F. Goodrich Big Three Inds. Blair, John Bliss Laughlin Boeing' Borg Warner Baxter Travenol Labs. Braniff Brockway Glass Brunswick Burndy Codence Industries Carlisle Callahan Mining Capital Cities Communications CBS Charter Cheseborough Pond Chrysler Cluett Peabody Coca Cola, NY Colgate Palmolive Combustion Engineering Conrac Continental Group Conwood Cooper Industries Cordura CFC Industries Crouse Hinds 126 Crown Cork and Seal Cummins Curtis Wright Dennison Dentsply DeSoto Dexter Diamond International Drehold DiGiorgio Donnelly Dorsey Dow Chemicals Eaton Easco EG&G Emhart Fairchild Industries Federal Mogul Federal Signal. Fieldcrest Mills Fischer Scientific FMC Ford Motor Fort Howard Paper Foster Wheeler Fruehauf GATX Gateway Industries General Dynamics General Motors Genearl Signal Genstar G.F. Business Equipment Giddings Lewis Gifford Hill Gillette Ginas Gleason Works Goodyear Tire Greyhound Grumman Gulf Research and Chemical Hanna Mining Harcourt Brace & Jovanovich Hazeltine Heileman Brewing Hershey Hesston Homestake Mining Host 127 Hospital Corp. of America Hudson Bay Mining I.C. Industries Illinois Tool Works Inexco Oil Ingredient Technology International Flavors I.U. International Corp. Johnson & Johnson Jorgensen, Earle Kane Miller Kellogg Kerr McGee Kennecott Copper Knight Ridder Lamson Sessions Lenox Lilly, Eli Lionel LTV Corp. Lynch Communications Masco McNeil Corp. MEI Corp. Melville Mesta Machine Mirro Mohasco Mohawk Rubber Monarch Machine Tool Moore McCormack Morrison Knudson Munsingwear Myers Nashua National Can National City Lines National Gypsum North American Coal North American Phillips Northrop Norton Nucor Oak Industries Oakite Products Occidental Petroleum Ogden Phelps Dodge Pitney Bowes Porter Potlatch Reichhold Chemical Revere Copper & Brass Revlon Robertson, H.H. Robins, A.H. Rubbermaid Ryder System Saint Joe Minerals Schaefer, F.M. Scheving Plough Schlitz Sealed Power Searle, G.D. Sherwin Williams Signal Signode Simmonds Precision Smith International Southland Southwest Industries SPS Technologies Standard Brands Stanley Works Stone Container Sun Chemical Sunstrand Swank Sybron Teleprompter Thiokol Thomas & Betts Thomas-Industries Time, Inc. Times Mirror Transway International TRW Tyler Corp. UMC Industries United Refining United Technologies Upjohn U.S. Industries VF Corporation Wallace Murray Warner Communications Warner Lambert Wayne Gossard Wean Limited Wheelabrator Frye Whirlpool White Motor Witco Chemical Wrigley WR Grace Appendix D Parameter specifications for hypothesized model A -X la: .3 64—! O 0 0 0 0 0 0 0 o o o o 7 0 4 8 0 9 o 10 0 o 11 O 12 o 13 |-1 128 25 27 I19- 28 33 34 I o 35 36 129 37 38 |~e 30 x9 x10 x11 x12 x13 39 0 40 o 0 41 0 0 0 42 0 0 0 0 43 Parameter specifications for hypothesized measurement model le- 14 15 17 16 18 19 11 12 13 O Appendix E 130 22 23 24 25 131 26 27 28 29 11 12 13 30 0 31 0 0 32 Parameter specifications for measurement model M2 -X lo- 10 11 l3 l6 17 21 26 18 22 27 19 23 28 Appendix F 24 29 132 30 [<3 10 ll 12 13 32 33 133 39 10 40 ll 12 13 41 0 42 0 0 43 Appendix G Parameter specifications for prediction model P 3' £1 £2 £3 £4 55 Equation 1 10 ll 12 13 14 Equation 2 l7 l8 19 20 21 1’. Equation 1 Equation 2 Equation 1 45 Equation 2 0 46 134 15 22 16 23 Appendix H Parameter specifications for prediction model P2 .9; n1 n2 Equation 1 (1.0) Equation 2 10 (1.0) 3 . £1 £2 £3 £4 £5 £6 £7 Equation 1 11 12 l3 14 15 16 17 Equation 2 18 19 20 21 22 23 24 3‘. Equation 1 Equation 2 Equation 1 46 Equation 2 O 47 135 Appendix J Parameter specifications for prediction model P4 .3. n1 r‘2 Equation 1 1.0 Equation 2 17 1.0 E. £1 £2 £3 £4 £5 £6 57 Equation 1 18 19 20 0 0 21 0 Equation 2 22 23 0 O 24 25 0 1’. Equation 1 Equation 2 Equation 1 47 Equation 2 O 48 137 Appendix K Lower left triangle of correlation matrix for coefficients of saturated model: Fixed X - Model 14 .2 2 1 4 5 4 2 4 9 10 11 12 11 14 15 14 12 14 '21 '11 '12 '12 '14 '15 '16 ‘12 '14 '19 '110 '111 '112 '111 ‘21 '22 '21 '24 "21 1.000 '11 -.000 1.000 '12 .000 ~.292 1.000 ‘15 -.000 .122 -.592 1.000 '14 .000 .551 .045 -.1s: 1.000 ‘19 .. -.254 -.152 .244 -.496 1.0011 '14 ..000 -.110 .111 -.1:0 .020 -.026 1.000 '12 .000 .114 ~.041 .010 .225 -.154 -.292 1.000 '19 -.000 -.109 .201 -.134 -.029 -.014 .244 -.2;14 1.000 '19 -.000 .005 ~.150 .100 -.259 .521 ~.052 -.292 ~.042 1.000 ‘110 ~.000 .045 -.014 -.015 .013 -.03: .129 -.414 .102 .040 1000 ‘m .000 -.091 -.064 .450 -.220 .1112 -.094 -.114 .049 .021 -.045 1.000 '212 -. -.214 .294 -.111 .044 -.106 .111 -.250 .199 -.044 .051 -.141 1.000 '125 -.000 .254 ..244 -.m .044 -.029 .154 ..205 .200 .015 .154 -.405 -.038 1.000 '21 -.054 -.000 .0011 -.000 -.000 .000 .000 -. .000 .000 .000 .000 .000 -.000 1.1200 '22 ..022 .000 ..000 .000 -.000 .000 -.000 .000 -.000 .000 -. .000 -.000 .000 ..292 1.000 '25 .024 -. .000 -. .000 ..000 .000 .000 -.000 -.000 -.000 ..000 .000 -. .112 -.199 1.000 '24 .025 -.000 -. .000 -. .000 -. .000 -. ~.000 -. .000 .000 -.000 .145 .042 -.525 1.000 1 2 1 4 5 4 2 4 9 10 11 12 11 14 u 14 12 14 ‘21 ‘11 '12 '11 ’1. ‘15 '14 '12 '14 '19 7110 '2:1 ‘112 ’11) '21 '22 '23 '24 '25 -.055 .000 .000 -.000 .000 -.000 .000 .000 .000 -.000 .000 -.000 .000 .000 .255 -.112 .242 -.444 '24 —.029 .000 -.000 .000 -.000 .000 -. .000 -.000 .000 - 000 .000 -. -.000 -.104 .110 -.122 .024 '22 .101 ~.000 .0110 -.000 -. .000 .000 -.000 .000 -. .000 .000 .000 .000 .110 -.022 .012 .251 '29 ~.049 .000 -. .000 .000 .000 - 000 .000 -.000 .000 -. -.000 -.000 -.000 -.105 .200 -.:52 -.032 '29 .144 -.000 .000 -.000 .000 -.000 -. .000 ..000 -.000 -.000 -.000 .000 -.000 -.001 -.145 .110 -.225 '210 -.112 -.000 -.000 .01.: ..000 .000 .000 .000 .000 .000 -.000 .000 -. .000 .050 -.021 -.043 .004 '21: .014 .000 .000 ~.0oo .000 -.000 .000 .000 -. -. .000 ~.000 .000 .000 -.094 -.045 .449 -.249 '212 -.050 .000 ..000 .000 -.000 .000 -.000 .000 -.000 .000 ..000 .000 -.000 .000 -.215 .292 -.155 .059 '21) -.051 -. .0130 .000 -.000 .000 -.000 .000 -.000 .000 -.000 .000 ~.000 -.000 .254 -.242 -.121 .041 59 20 21 22 29 24 25 24 22 115 126 127 91! 129 1210 2211 2212 7213 '25 2.000 '24 -.025 1.000 '22 -.2.19 -.294 1.000 '24 ~.014 .242 -.241 1.000 '29 .314 ..041 -.224 ..091 1.000 '210 ~.050 .121 -.421 .102 .011 1.0110 '221 .144 4.094 -.114 .032 .025 -.044 1.000 '21: -.105 .152 ~.259 .191 -.054 .069 -.111 1.000 '21) -.012 .150 -.200 .210 .002 .101 -.401 -.015 1.000 138 BIBLIOGRAPHY Bibliographz Abdel-khalik, A. 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