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001247981

BEBRFACULTY WORKINGPAPER NO. 1476

Financial Ratios, Fundamental Firm Characteristics,

and Measurement Models: Issues and Evidence

Thomas J. Frecka

David A. Ziebart

College of Commerce and Business Administration

Bureau of Economic and Business ResearchUniversity of Illinois, Urbana-Champaign

BEBRFACULTY WORKING PAPER NO. 1476

College of Commerce and Business Administration

University of Illinois at Urbana -Champaign

August 1988

Financial Ratios, Fundamental Firm Characteristics, andMeasurement Models: Issues and Evidence

Thomas J. Frecka, Associate ProfessorDepartment of Accountancy

David A. Ziebart, Assistant ProfessorDepartment of Accountancy

Financial support for this project was provided by theDepartment of Accountancy and the Bureau of Economic andBusiness Research of the University of Illinois at Urbana-Champaign. We appreciate comments provided by participants inthe Accountancy Forum at the University of Illinois.

Do not quote. Comments are welcome.

Digitized by the Internet Archive

in 2011 with funding from

University of Illinois Urbana-Champaign

http://www.archive.org/details/financialratiosf1476frec

Financial Ratios, Fundamental Firm Characteristics , andMeasurement Models: Issues and Evidence

Abstract

This study examines the relationships among a firm's

financial ratios and its underlying financial dimensions using a

measurement model approach. Both exploratory and confirmatory

factor analytic techniques are used to link observable financial

ratios to underlying fundamental dimensions. This study

illustrates a causal modeling approach for evaluating the

representativeness of financial ratios as measures of underlying

firm attributes.

KEY WORDS: Financial ratios; Factor analysis; Causal Models;

Measurement Models: Covariance structures.

Financial Ratios, Fundamental Fira Characteristics, andMeasurement Models: Issues and Evidence

I . I ntroduction

The purpose of this study is to examine the relationships among a

firm's financial ratios and that firm's underlying financial dimensions

using a causal measurement model approach. Financial ratios are

empirically linked to underlying fundamental economic dimensions using

both exploratory and confirmatory techniques. Accordingly, this study

will illustrate a causal modeling approach for evaluating the

representativeness of financial ratios as measures of underlying firm

attributes. In addition, the differences between exploratory and

confirmatory methods will be discussed and illustrated.

A causal model portrays the causal links and chains between the

various components of the process researched (Abdel-Khalik and Ajinkya

[1979, pp. 20-23]). It is unique in its effort to develop a structural

network of causal relationships built upon theoretical underpinnings.

In the causal modeling process a model structure is developed and the

estimation solution is constrained by the parameter requirements of the

theoretical structure. For this study, this means that certain

financial ratios are constrained to load on certain underlying

fundamental financial dimensions (such as liquidity, leverage, or

profitability) and not load on others. This portrays a measurement

structure in which the observed financial ratios are measures of the

unobservable fundamental dimensions. These links between the observed

financial ratios and the underlying financial dimension are

hypothesized, estimated, and tested.

The importance or a causal moaeiing approacn in tnis rinanciai

ratio context relates to how we use ratios to understand the economic

attributes of the firm, how such attributes change over time, or how the

attributes compare with those of other firms. An appreciation of the

underlying dimensions that certain financial ratios measure is important

in a variety of decision contexts including the effects of firm

attributes on the risk and return of securities, on the terms of lending

agreements, or on the evaluation of the relative financial health of a

firm. Determination of the ratios which best measure certain financial

dimensions would enhance the usefulness of ratio analysis and provide

insight into the propriety of using alternative ratios to measure the

same underlying firm dimension.

Traditionally, economic attributes such as liquidity, leverage,

profitability, and activity have been used to portray and evaluate the

financial condition and performance of the firm. Financial ratios have

been constructed to measure these attributes and a number of financial

ratios are purported to measure them. In general, these attributes are

not precisely defined, not directly observable, and not directly linked

by deductive theory to the types of decisions contexts mentioned above.

In addition, the degree of measurement error inherent in various

financial ratios as measures of the underlying attributes has not been

previously assessed.

Since it is not possible to directly observe the economic dimension

of the firm, financial ratios are commonly used as the indicators or

measures of the unobservable financial dimensions of interest. Given a

measurement theory perspective, each financial ratio can be viewed as a

linear combination of the underlying economic dimension and an error of

measurement component.

Given the lack of precise definitions for the source variables (the

constructs which represent various financial dimensions of a firm), it

is not surprising that a large number of financial ratios have been

proposed to measure the financial attributes of the firm. However, the

suitability of the various financial ratios as measures of the

underlying economic dimensions of a firm has not been ascertained. The

validity of a financial ratio as a measure of an underlying financial

dimension is dependent upon the ratio's representativeness (the degree

to which the observed ratio is a measure of a particular dimension and

pnot another dimension) and the degree of measurement error.

In describing the process of identifying "useful" ratios as it

developed in the 1930's, Horrigan [1968] states:

"In this approach, a priori analysis and/orempirical evidence were rarely provided to substantiatean author's claim that his particular selection of ratiosrepresented an efficient collection of ratios for analyzingfinancial statements. Rather, the author's group of

selected ratios — and sometimes accompanying absolute andrelative criteria — were promulgated solely on theauthority of his experience in statement analysis." (p. 288)

Later, "usefulness" was evaluated on the basis of a financial ratio's

ability to predict or explain economic phenomena such as bankruptcy or

security returns. However, if one considers that it is the underlying

firm dimension, measured by the financial ratio, which is the attribute

of interest, then the measurement error issue is critical. In

situations in which the financial ratio is significantly imprecise,

(significant measurement error exists) the usefulness of that ratio in

explaining or predicting the event of interest may be largely

diminished. In these situations one encounters the traditional errors-

in-variables problem.

Given the potential for a large number of ratios, the idea that the

underlying constructs are of interest, and the benefits of parsimony,

various data reduction techniques have been employed. Unfortunately,

these reduction techniques have been based on statistical analyses void

of theoretical underpinnings and measurement structure considerations.

The most widely used technique in the data reduction studies is

exploratory factor analysis. Examples include Pinches and Mingo [1973],

Libby [1975], and Gombola and Ketz [1983]. Unfortunately, an

exploratory approach is significantly limited in its ability to

determine the appropriate measurement structure and to evaluate the

propriety of alternative model configurations.

An approach that allows testing of alternative measurement

configurations is confir matory or restricted factor analysis. Its

primary advantage is that it allows one to test specific hypotheses

regarding the measurement structure. In this study, we compare and

contrast the application of exploratory and confirmatory approaches.

The use of an exploratory approach in earlier studies can not be

criticized. It was not until the late 1960's that both computer

hardware and software were reasonably available for conducting

exploratory analyses (Jackson and Borgatta [1981]). The ready

availability of algorithms to estimate restricted or confirmatory factor

analysis models and the inclusion of the confirmatory approach in

standard statistics texts is a rather recent development (Marridi

[1981]). For example, the maximum likelihood estimation procedure used

in this study was introduced by Joreskog in 1973 and only became widely

available in the late 1970's.^ Recently, confirmatory factor analytic

methods and procedures have been added to widely used user-friendly

statistical packages such as SPSS Fornell [1982] refers to these

confirmatory techniques as "a second generation of multivariate

analysis .

"

In this study, we initially conduct an exploratory analysis.

Alternative exploratory measurement models are presented and evaluated.

We subsequently conduct a confirmatory analysis. In our confirmatory

analysis we hypothesize a particular measurement model configuration,

estimate the model parameters, and then test both the individual

parameters and the overall model configuration. Alternative

measurement model configurations are then estimated, tested, and

evaluated. We then compare and contrast the confirmatory results with

the exploratory results.

From the results we answer the following questions:

(1) What are the underlying dimensions of the data; i.e., what are

the appropriate factors, the ratios that measure each factor, and what

is the number of factors that reasonably explains the observed ratios;

(2) Are the underlying factors correlated, or linked in some way;

(3) Are the underlying factors well specified; i.e. , do the ratios

load significantly on the factors they purport to measure;

(4) Which of the ratios that measure a given factor is the "best"

measure; i.e., it has the smallest measurement error; and,

(5) Does the observed covariation among the ratios lend credence to

the hypothesized measurement structure?

The importance of this research relates to what we can learn from

using a formal measurement model to represent the relationships among

financial ratios and the underlying financial dimensions. Unlike

previous studies which have used only exploratory techniques described

as "brute empiricism," our study statistically tests the fit of the

measurement model structures through over-identification and compares

5

the results to those obtained using the traditional exploratory

approach. In general, the results from our confirmatory analysis

provide greater insight concerning the ratios that are needed to capture

the underlying economic dimensions of the firm.

We find that the underlying financial dimensions are correlated.

This result contrasts with most exploratory studies which have assumed

that the underlying factors are orthogonal. Further, while our analysis

leads to the same number of factors using both exploratory and

confirmatory approaches, the implied measurement model structures are

substantially different. Another notable result is that the underlying

size dimension is significantly correlated with the other dimensions.

This is surprising since ratios are espoused as a method to control for

size differences across firms. Our results indicate that the size

dimension is positively correlated with the profitability, cash flow,

activity, and capital structure dimensions and negatively correlated

with the liquidity dimension.

The remainder of the paper is organized as follows. Part II

provides a description of the measurement theory approach that is

inherent in confirmatory factor analysis and a description of the

modeling process. In part III we describe the data and the empirical

results. Part IV is a summary and includes suggestions for further

research.

II . Measurement Models - Techniques and Issues

A measurement model can be depicted as a set of underlying

constructs or factors in which the observable measures or indicators are

a linear function linking the observable indicators to the factors.

This relationship can be conceptualized as:

x = L X + e

where x is the vector of observable measures, X is the vector of

unobservable constructs, L is a matrix of regressors linking x to X, and

e is a matrix of measurement errors. The variables are assumed to be

mean deviated so that there is no intercept term in the expression.

It is important to note that this illustration of a measurement

model, while depicted in a regression framework, is fundamentally

different from a regression. In a normal regression situation, the x

and X variables are both observable and one attempts to estimate the

regressor L. In a measurement model analysis the x are observable but

the X are not observable. This implies that in addition to estimating L

and e one must also estimate the unobservable factors X. In this

study, the x are financial ratios, the X are the underlying

financial dimensions, and the e are the measurement errors of the ratios

as measures of the dimensions.

Two different approaches can be taken regarding the estimation of

the underlying measurement structure linking the observable variables to

the unobservable constructs. The approach used in most previous studies

of financial ratios is to conduct an exploratory factor analysis or

principal components analysis. This traditional approach places

relatively few, if any, restrictions on the measurement structure

configuration and lets the data delineate the implied measurement

model

.

Unfortunately, the application of a truly exploratory approach may

lead to an implied measurement model structure which violates both the

postulate of factorial causation and the postulate of parsimony (Kim and

Mueller, [1978] pp. 43-45). These two postulates are neccessary to

minimize the seemingly unsurmountable uncertainties inherent in the

linkage between the factor (measurement model) structure and the

observed covariance structure of the data. The postulate of factorial

causation may be violated in a pure exploratory study since the model is

developed with little or no reference to substantive a priori knowledge

about the data or the model structure. Violation of the postulate of

parsimony may result in an exploratory analysis when one chooses a more

complex model over a consistent but more simplistic model. This may

occur because the exploratory analysis has failed to consider the latter

model configuration.

The postulate of factorial causation is based on the assumption that

the observed variables are linear combinations of the underlying factors

and that the covariation between the observed variables is the result of

the observed variables being linked to one or more common factors (Kim

and Mueller, [1978] p. 78). In essence, it is the underlying factors

which cause the observed covariation among the variables. The postulate

of parsimony requires that if two models equally explain the data, then

the simpler model is more appropriate (Kim and Mueller, [1978] p. 79).

The failure to consider the postulate of factorial causation can

result in a serious indeterminacy of one covariance structure but

various factor loadings. In a financial ratios context, this problem

results in the inability to specifically measure the linkage between a

particular financial ratio and the dimension it purports to measure. As

an example, one may be able to find alternative measurement structures

in which the sign and magnitude of the coefficient linking the observed

financial ratio to the underlying financial dimension construct is

dependent upon the rotation method employed in the analysis. Choice of

rotation method may be dependent upon a somewhat arbitrarily chosen

8

criterion. This results in an implied measurement configuration which

is the result of the criterion chosen rather than any theoretical

underpinnings

.

The second indeterminacy, related to the postulate of parsimony,

concerns the situation of one covariance structure but alternative

numbers of factors or measurement configurations. Normally in an

exploratory study, the number of factors in the final solution is based

on the magnitudes of the eigenvalues. The general rule of thumb is to

only include as factors the eigenvectors with eigenvalues greater than

or equal to one. The number of factors may be a somewhat arbitrary

choice and the resulting measurement model configuration is dependent

upon the choices made by the researcher either implicitly or explicitly.

In addition to the problems of factorial causation and parsimony,

the issue of an orthogonal versus an oblique solution can seriously

impact representative validity. With an orthogonal solution, the

approach used in most previous studies of financial ratios, the

underlying factors are assumed to be independent of each other. The

factors are allowed to covary and are not assumed to be independent when

an oblique solution is employed.

The application of factor analytic techniques without an

appreciation for the implied measurement configuration can be

problematic. Foster [1986] points out the potential difficulties of the

traditional exploratory approach:

Factor analysis can, if used in an uncritical manner,become brute empiricism in the extreme. However, whenused with recognition of its limitations (for example, thepotential excessive reliance on factors suggested by data)and of the judgement calls necessary in its application(for example, how many separate factors to identify), it

can be a useful addition to the tools used in financialstatement analysis.

The other approach to the empirical investigation of measurement

structures is a confirmatory approach. With this approach, a particular

causal structure is hypothesized and an a priori measurement model

configuration is imposed on the analysis; the number of factors, the

presence of covariation among the factors, and the determination of

which variables load on which factors are specified. A confirmatory

approach imposes a structure of factorial causation on the analysis.

Accordingly, specific hypotheses regarding the factor structure are

introduced into the analysis since parameters are specifically

constrained. The probability that the imposed structure will be

supported by the observed covariance structure is less, if factorial

causation is not in operation. 5 In a confirmatory analysis, the

parsimony issue usually does not arise since the number of factors is

based on theoretical underpinnings.

Figure 1 illustrates the exploratory and confirmatory approaches to

the empirical investigation of causal measurement structures.

INSERT FIGURE 1

Under an exploratory approach, the solution method, including rotation,

orthogonal versus oblique factors, and the method to determine the

number of factors must be considered. In many instances where "canned"

computer programs are used, these choices are constrained by the

program. In other instances, the researcher either implicitly or

explicitly choses the method without considering the implied

measurement structure.

In the first step of an exploratory study, the solution is computed

and an initial measurement model configuration is implied by the

results. The observed variables can then be regressed on all of the

10

factors found in the first step to determine the sensitivity of the

variables to changes in the factors. This regression step is

particularly useful if the analysis is not an orthogonal solution. For

an orthogonal solution the factor pattern matrix and the factor

structure matrix describe the correlations between the factors and the

variables. However, when an oblique solution is obtained the matrix of

coefficients do not represent the correlations. The measurement

configuration is suggested by the regression coefficients that are

statistically significant. This allows one to determine the

appropriate pattern matrix as well as "identify or name" the underlying

factors. Given that most exploratory models are "just-identified" or

even "under-identified" one cannot statistically test the underlying

measurement model structure. An exploratory approach can only provide

minimal self-validating information regarding the choice among

alternative measurement model configurations.

In contrast, Figure 1 illustrates that the confirmatory approach

hypothesizes a model structure as the basis for the analysis. The

factor analysis is then conducted within the solution constrained by the

hypothesized model configuration. By restricting the analysis such that

the number of factors and their loadings are tested on the sample data,

a confirmatory analysis can provide self-validation. By overidentifying

the model one can statistically evaluate the model configuration and

make comparisons to alternative structures.

The measurement model parameter matrices used throughout the

remainder of this paper are defined as follows:

L is an m by n matrix of the coefficients relating the latent

financial dimension to the observed financial ratio;

1 1

P is an n by n variance-covariance matrix for the latent

financial dimensions;

e is an m by m variance-covariance matrix for the measurement

errors

.

The specification of the parameters in each of these matrices

determines the measurement model configuration imposed on the analysis.

The loadings or pattern matrix, L, depicts the number of factors and

restricts which ratios load on which factor. In an exploratory analysis

all ratios are allowed to load on all factors, whereas in a confirmatory

analysis only selected ratios are allowed to load on particular factors.

For example, by specifying L to be an m by 8 matrix and also specifying

that every element of the matrix is estimated depicts that the

measurement model has 8 underlying financial dimensions and that each

financial ratio loads on each and every one of the underlying financial

dimensions

.

Through specification of the elements in the covariance matrix among

the factors, P, the factors can be restricted to be orthogonal (all of

the off-diagonal elements are restricted to be zero). Alternatively,

specifying P to be full and estimating all of the off-diagonals results

in an oblique solution.

The measurement error matrix, e, can be constrained to be full and

all elements estimated - this denotes that the underlying factors are

not the only systematic source of variation among the variables.

Constraining e such that only the diagonals are non-zero represents that

only the factors on which the variables load are the systematic sources

of variation among the variables. A number of very different

measurement model structures can be constructed through alternative

7specifications for the elements in the various parameter matrices.

12

III. Statistical Procedures and Results

The observable financial measures chosen for this study are a group

of eighteen financial ratios and three size measures. The sample

consists of December 31, 1985 year-end manufacturing firms across a

number of industries. To be included in the sample the firm must be

listed on the Compustat tape. The ratios and size measures chosen are

the following:

cash / current liabilitiescash / salescash / assetsquick ratiocurrent ratiocash flow / salescash flow / assetslong term debt / equitytotal debt / equityinterest coveragecash flow / interestnet income / salesnet income / equitynet income / assetsearnings per shareasset turnoverreceivable turnoverinventory turnoverassetssalesmarket value of equity

This set of financial ratios corresponds closely to the set (or a

subset) of the ratios previously studied by Stevens [1973], Johnson

[1979], or Gombola and Ketz [1983]. In addition, this set of ratios is

also representative of the ratios normally listed in a discussion of

financial statement analysis (see Foster [1986, pgs. 110-111 ] , Lev

[1974], or Van Home [1980]). Both the exploratory and confirmatory

analyses are conducted on this data set.

13

Statistical Procedures

The exploratory analysis uses SHAZAM with an orthogonal varimax

rotation for the solution and is conducted on the correlation matrix.

This choice of an orthogonal varimax solution is consistent with

previous exploratory studies. Although a quartimax rotation would

enhance the factorial interpretations of the observed financial ratios,

the use of a varimax rotation aids in the interpretation of the factors

and is the technique that has been previously applied in most of the

financial ratio literature.

For the confirmatory analysis, the statistical procedure is a Full

Information Maximum Likelihood (FIML) approach. The particular

estimation procedure chosen is LISREL: Analysis of Linear Structural

Relationships by the Method of M axi mum Likelihood by Joreskog and Sorbom

[1978]. This maximum likelihood estimation algorithm requires that the

variables be normally distributed so that the estimated parameter

coefficients as well as the overall model structure can be statistically

tested. This requirement is not neccessary for the exploratory

analysis; however, since we wish to compare the results of the

exploratory and confirmatory analyses the normalized sample is used for

both.

To normalize the data, a logarithmic transformation is applied to

all of the ratios and then the distributions are trimmed, as suggested

by Gnanadesikan [1977, pgs. 121-195] , to provide robust estimates of the

means and variances. 9 The distribution for each ratio is then tested

for normality using the omnibus test (based on skewness and kurtosis)

suggested by Bowman and Shenton [1975]. All of the distributions for

the individual ratios meet the omnibus test for normality criteria at a

level of .05 or better. The preliminary sample consists of 425 firms

14

before trimming. A large number of firms are deleted from the sample

since a firm must be eliminated if an observation on any one of the 21

financial ratios is deemed an outlier. The normalizing of the data

reduces the sample to 193.

Exploratory Analysis

In order to demonstrate the benefits of a theory-derived

confirmatory approach, we present the exploratory analysis first. In

the exploratory analysis no measurement structure is considered "a

priori" and the implied measurement model structure is completely data

derived. Glymour, et. al. [1987] note that exploratory factor analysis

"does not incorporate any of the user's prior knowledge about the causal

process that generates the data."

Using a simple principal components procedure, the eigenvalues and

the cumulative percentages of variation explained by the eigenvalues are

provided in Table 1.

INSERT TABLE 1

Note that the general rule of thumb regarding the appropriate number of

factors to retain in the final solution is to include a factor only if

its eigenvalue is equal to or greater than one. This means that the

factor must explain more than its own proportional variation.

Application of this criteria results in six factors retained for our

data set.

Once the number of factors has been determined, the next step is to

choose the method to be employed in the simplification of the factor

structure. This involves the choice of an oblique solution versus an

orthogonal solution. In addition, the choice of the rotation method to

be applied to the axis must be made. An orthogonal solution is chosen

15

since most previous exploratory studies have used it. A varimax

rotation is employed in order to be consistent with previous studies.

Based on these choices, we estimate the exploratory measurement

model configuration; a six factor model in which the factors are

constrained to be independent. 10 The next step is a regression of the

observed financial ratios on the six estimated orthogonal factors. This

regression allows an assessment of the implied measurement model through

an indication of the degree to which the variations in the observed

ratios are explained by the six factors they are purported to measure.

Note that this model depicts each ratio as measuring all of the

underlying factors since each ratio is regressed on all of the

factors. The results of these regressions are provided in Table 2.

INSERT TABLE 2

In order to have a more meaningful measurement model, a measurement

structure linking individual financial ratios to particular individual

factors (rather than all of the factors) must be imposed. The choice of

the ratio that is to be modeled as an indicator of a particular

underlying dimension can be made in two ways. From a purely exploratory

point of view, one can base this choice on the magnitude of the

correlation between the ratios and the factors regardless of the sign.

An alternative approach, which assumes that the covariation between the

underlying factor and its measure should be positive, is based on the

degree of positive correlation. Some previous studies have used only

the positive factor loadings while others like Johnson [1979] have used

both positive and negative loadings.

A measurement structure configuration based on the degree of

correlation, regardless of sign, between the ratio and the underlying

16

factor is depicted in Figure 2. This model is labeled El.

INSERT FIGURE 2

Note that this measurement structure is very different than one might

expect. It loads ratios that are purported to measure very different

attributes of the firm on the same factor. Two of the six factors do

not show any ratios loading on them. This result is due to using the

magnitude of the correlation between the ratio and the factor employed

to determine the loadings. For instance, the cash flow to sales ratio

is loaded on factor one and has a correlation on -.968, the correlation

with factor six is -.964. Likewise, the receivable turnover ratio has a

correlation of -.554 with factor 1 and .553 with factor two. It is

difficult to compare these results to those of previous studies since

most previous studies only report the single factor loading that the

researcher has chosen; factor loadings of the ratios with other factors

are not provided.

Model E2, based on the magnitude of the positive correlation between

individual ratios and the factors, is depicted in Figure 3. In this

case, no ratio loads on factor five.

INSERT FIGURE 3

For some of the ratios the use of absolute correlations versus

positive correlations makes little difference. The factors chosen for

the ratios to measure are the same under both methods for the following

ratios

:

cash / current liabilities,cash / sales,cash / assets,quick ratio,current ratio,inventory turnover.

17

In order to determine the extent to which the ratios are adequate

measures of the underlying factors we regressed each ratio on the factor

with (1) the largest absolute correlation, and (2) the largest positive

correlation. These results are provided in Table 3.

INSERT TABLE 3

A comparison of the two implied exploratory models, El and E2, shows

significant differences in both the representativeness of the ratios and

the proportion of variation in the ratios explained by the underlying

factor.

Confirmatory Analysis

We initially use an a priori measurement model configuration

suggested by Foster [1986 pgs. 58-70]. This structure has eight factors

which underlie the set of financial ratios used in this study. The

eight factors (underlying economic dimensions of the firm) and the

associated financial ratio measures are as follows (the numbers, 1-21,

associated with each of the ratios will be used rather than the names of

the ratios throughout the remainder of this paper):

Cash position :

1. cash / current liabilities2. cash / sales3. cash / assets

Liquidity :

4. quick ratio5. current ratio

Cash Flow :

6. cash flow / sales7. cash flow / assets

Capital Structure8. long term debt / equity9. total debt / equity

Debt coverage :

10. interest coverage11. cash flow / interest

18

Profitability :

12. net income / sales

13. net income / equity14. net income / assets15. earnings per share

Turnover or activity :

16. asset turnover17. receivable turnover18. inventory turnover

Size :

19. assets20. sales21. market value of equity

In the first confirmatory analysis, the underlying financial

dimensions are assumed to be independent of each other and the financial

ratios are allowed to load only on the dimensions they are intended to

measure. This assumption is consistent with the previous work of

Stevens [1973], Johnson [1979], and Hopwood and Schaefer [1986]). The

parameter matrices which represent this model, Ml, are as follows:

L=

Xl

X2

X3

X4

X5

X6

x7

X8

xl

Ll

X2 L

2x3

L3x4

L4

x5 L5

X6 L

6x? L?x8 L8x9 L9

x 10 L 10x ll L llx12 L 12

x13 L 13x 14 L 14x15 L 15

x 16 ^16x 17 L 17x18 L

18x 19 L 19x 20 L20x21 L21

P(8 by 8) = identity matrix

e(21 by 21) = identity matrix

19

This model is depicted graphically in Figure 4 and it illustrates that

the e's are uncorrelated. This means that the underlying factors are

the only systematic source of variation in the observed ratios.

INSERT FIGURE 4

Model Ml is tested for goodness of fit using a chi-squared test.

This test is applied to determine the model's ability to create a

covariance matrix, S«, that replicates the observed covariance matrix,

So. The chi-squared value for Ml is 4365.5 (189 degrees of freedom).

This high chi-squared value indicates that the measurement structure is

a poor representation of the causal structure underlying the observed

covariation among the financial ratios.

However, as Joreskog and Sorbom [1979] and Bentler and Bonet [1980]

point out, sample size may bias the chi-squared value and lead to

incorrect conclusions. A preferable procedure is to perform incre mental

fit tests based on a comparison of alternative measurement models.

Since the difference in chi-square values for two different model

configurations is also asymptotically distributed as a chi-square

variate, the hypothesis of equivalence between the two model structures

can be tested. We utilize this test procedure below.

An appropriate comparison is to evaluate Ml in relation to a null

model, Mn, defined as a restricted model with no structure implied;

i.e., the elements of L are all set to zero. The chi-square value for

the null model is 8062.9 (210 degrees of freedom). The hypothesis of

model equivalence is rejected at a very high level of significance.

A measure of the proportion of the generalized variance inherent in

the observed data set which is explained by a model, the nor med fir

index , can be computed (Bentler and Bonet [1980]). The normed fit index

20

for Ml is (1 - 4365.5/8069.9), or 46%. The normed fit index can be

interpreted similarly to the coefficient of determination; 46 per cent

of the generalized variation in the observed variance/covariance matrix

is explained by the hypothesized model structure.

As indicated previously, Ml and most of the previous research

(Stevens [1973], Johnson [1979], or Hopwood and Schaefer [1986]) have

assumed that the financial dimensions are uncorrelated. It is very

difficult to justify this assumption given the inter-relationships among

the financing, investing, and operating activities of a firm which are

captured by the underlying financial dimensions. For example, it is

unrealistic to assume that the profitability dimension and the turnover

(activity) dimension are unrelated or that the cash flow dimension is

not correlated with the turnover dimension.

Our second confirmatory model, M2, utilizes the same specifications

for L and e as Ml but allows the underlying financial dimensions to

covary; P is specified to be symetric and full with all of the off-

diagonal elements estimated. This model is depicted in Figure 5.

INSERT FIGURE 5

The chi-square value for M2 is 3661.9241 with 161 degrees of freedom.

Given that more parameters are being estimated, the incremental fit

needs to be assessed since one expects the fit of the model to improve.

M2 has a normed fit index of 55% (recall that the normed fit index for

Ml is 46%). A comparison of M2 to Ml can be made using the same

approach that was used to compare Ml to Mn. This comparison assesses

the propriety of the orthogonality assumption. The null hypothesis of

model equivalence between Ml and M2 is rejected at a significance level

better than .005, based on a chi-squared variate of 704 with 28 degrees

of freedom. This result indicates that the orthogonality assumption is

21

unwaranted. A measurement model allowing covariation among the

underlying financial dimensions is a significant improvement over an

orthogonal model.

However, the adequacy of a model configuration is dependent upon the

individual parameter estimates as well as the overall fit of the model.

The parameter estimates and t-ratios for M2 are provided in Table 4.

INSERT TABLE 4

The parameter estimates indicate some problems with M2. Given that the

analysis is conducted on the correlation matrix, the parameter estimates

for L, P, and e should be less than or equal to 1.00. Note that the

estimates for L5 , L

18 , e5> and e lgare significantly greater than 1.00.

In addition, the estimates for L«g, L 17 , and L«g are insignificant.

This suggests that although the overall model fit seems to indicate a

representative model, some of the parameter estimates are not allowable

and the model structure may be misspecif ied.

Given the difficulties with the M2 parameter estimates, we estimate

an alternative model, M3. This model combines the cash position

dimension of Ml and M2 with the liquidity dimension. This seems

appropriate since cash represents the most liquid asset of a firm. The

debt coverage dimension of Ml and M2 is eliminated in M3. The interest

coverage ratio is a measure of profitability while the cash flow to

interest ratio is a measure of cash flow. These changes decrease

the number factors to six. Note that this is consistent with the number

of factors in the exploratory analysis. M3 is a six factor model in

which the six factors and the associated measures are the following:

22

Profitabilityinterest coverage (x 10 )

net income / sales (x-^)

net income / equity (* 13 )

net income / assets (x^)earnings per share (Xj

5 )

Liquiditycash / current liabilities (Xj)

cash / sales (x2 )

cash / assets (Xg)

quick ratio (x^)

current ratio (x5 )

Cash Flowcash flow / sales (x

g )

cash flow / assets (x-7)

cash flow / interest (X11)

Activityasset turnover (x^g)

receivable turnover (x-jy)

inventory turnover (Xjg)

Sizeassets (xiq)

sales (x2q)

market value of equity (x,i)

Leveragelong term debt / equity (Xg)

total debt / equity (xg)

Each factor is allowed to covary with the other factors. Figure 6

represents this configuration.

INSERT FIGURE 6

The chi-squared value is 4032.406 with 175 degrees of freedom. A

comparison to the null model (Mn) results in the hypothesis of

equivalence being rejected. The incremental fit index indicates that

M3 recreates 50% of the generalized variation in the observed data

matrix. A comparison to M2 indicates that the overall fit of the model

is somewhat poorer; however, the individual parameter estimates are all

appropriate. The factor loading coefficients are all less than or equal

to one and they are all statistically significant except the coefficient

23

linking the asset turnover ratio to the activity dimension. The

parameter estimates for M3 are provided in Table 5.

INSERT TABLE 5

In M3 the factors are allowed to covary. The off-diagonals of the P

matrix indicate that many of the factors are correlated at fairly high

levels. Profitability is positively correlated with liquidity and cash

flow and negatively correlated with leverage. The second factor,

liquidity, is positively correlated with profitability and cash flow and

negatively correlated with leverage. While being positively correlated

with profitability and liquidity, cash flow is also positively

correlated with both size and activity and negatively associated with

leverage. The size dimension is linked positively with cash flow and

activity. The leverage dimension is negatively correlated with

profitability, liquidity, and cash flow.

The covariation between size and the other five factors is of

significant interest. Financial ratios are expected to control for

size differences among firms yet these results indicate that size is

correlated with the other dimensions. To assess the significance of

the covariation between size and the other dimensions, M3 is re-

estimated constraining the size dimension to be orthogonal to the other

five dimensions. The resulting chi-square value for the modified model

is 4078.43 with 180 degrees of freedom. Orthogonalizing the size

dimension results in a model that fits significantly poorer (4078.43

with 180 degrees of freedom compared to 4032.406 with 175 degrees of

freedom.

The matrix that represents the proportion of the variation in the

observed ratios which is not explained by the underlying factor is e.

An analysis of the elements in this matrix indicates that the underlying

24

dimension explains a significant proportion of the variation in the

observed financial measures. It also indicates that the degree of

measurement error varies significantly across the different ratios as

well as across the underlying dimensions. The measurement error

variance is less than 10% in eight instances, between 10% and 50% in six

instances, and greater than 50% for the remaining seven measures.

The magnitudes of the t-statistics for the measurement coefficients

and the magnitudes of the measurement error variances portray the

"representative faithfulness" of the individual ratios as measures of

the underlying financial dimensions. The "best" measure for

prof itabiltiy is the net income to assets ratio. Earnings per share has

the greatest measurement error of any of the ratios used to measure

profitability.

For liquidity there are three ratios that are indicated to be very

adequate measures; cash to current liabilities, cash to sales, and cash

to assets. The cash to assets ratio has the smallest error variance.

Unfortunately, the two more traditional liquidity measures, the quick

ratio and the current ratio, have larger error variances than the cash-

based ratios.

The "best" indicator of cash flow is the cash flow to assets ratio

while the best measure of the size dimension is total assets. The

activity dimension does not seem to be well specified and it is not

measured very well by any of the three ratios. The inventory turnover

ratio has the smallest error variance. The long term debt to equity

ratio has the smallest error variance of the leverage measures.

These results indicate that certain ratios may be better measures

of the underlying economic dimensions than other ratios. Therefore, in

25

choices regarding the ratios to use for firm evaluation, prediction, or

explanation purposes, one should consider the measurement error issue

and choose the ratio with the smaller measurement error. This will

reduce the measurement error problem and enhance the ability to observe

significant coefficients. The underlying financial dimensions and the

financial ratio with the smallest measurement error variance are listed

in Table 6.

INSERT TABLE 6

To further pursue the postulate of parsimony, iterative model

building is undertaken to determine if simpler models can be found that

represent the data as well as M3. In this process, alternative causal

measurement model configurations are estimated and tested. Based on the

results of the simpler models, certain restrictions are relaxed (a more

complex model is developed), the model is again estimated and the chi-

squared value is obtained. A list of the various measurement model

configurations we examine, a short description, and the associated chi-

squared values are provided in Table 7.

INSERT TABLE 7

Mil may be a better representation of the underlying measurement

structure than M3. However, Mil has 5 underlying financial dimensions

and aggregates the activity ratios along with the leverage ratios.

Empirically, these two sets of ratios may be highly correlated but

theoretically they measure very different aspects of the firm. The

normed fit index for Mil is 51%, an insignificant improvement over the

50% for M3.

In the application of causal modeling techniques, the choice of the

most appropriate model must be based not only on the statistical

properties but also theoretical and conceptual underpinnings. Model fit

26

can almost always be improved by relaxing the model structure and

estimating additional parameters. Unfortunately, the model can be

relaxed to the degree that the results are sample dependent and the

parameters have no meaning. Given our data, it appears M3 provides a

reasonable fit from a total model perspective, the coefficient estimates

are appropriate, the model is relatively parsimonious, and the model

seems congruent with theory.

In summary, our confirmatory results indicate that a six factor

oblique model adequately represents the causal measurement structure

underlying the set of financial ratios chosen for this study. The six

latent financial dimensions in the model are: profitability, liquidity,

leverage, activity, cash flow, and size. The model is more parsimonious

than some other model choices; six factors versus eight factors, and the

results indicate that the assumption regarding independence among the

financial dimensions (as presumed in most previous studies) is

unwarranted both theoretically and empirically.

Comparison of Confirmatory versus Exploratory Results

Recall that in the confirmatory analysis we estimate the measurement

error variance for each of the twenty-one financial measures. In order

to compare the measurement error variances of the confirmatory model M3

to the exploratory model E2, the measurement error variances for the

exploratory model are computed as 1 - r . As the error component gets

larger (the correlation between the ratio and the factor get smaller)

the ratio becomes a less valid measure of the underlying factor. A

comparison of the error variances for M3 to those of E2 is provided in

Table 8. This provides some insights into the differences between the

27

data derived exploratory model and the confirmatory model based upon

theoretical underpinnings.

INSERT TABLE 8

In the theory-based measurement model M3, the underlying factor

explains a greater proportion of the variation in the individual ratios

than the exploratory model E2 for all but three of the financial ratios.

These three cases are the quick ratio, the current ratio, and the asset

turnover ratio.

The chi-squared value for M3 is 4032.406 with 175 degrees of

freedom. We can conduct a statistical comparison of the exploratory

models, El and E2, with M3 by computing the chi-squared values for

them. The chi-squared value for El is 6169.659 with 189 degrees of

freedom while the chi-squared value for E2 is 5268.087 with 189 degrees

of freedom. Both El and E2 are significantly poorer fitting models

than the confirmatory model M3. El and E2 have normed fit indices of

.24 and .35, respectively, whereas M3 has a normed fit index of .50.

M3 is more consistent with the observed covariance structure in the

data.

IV. Conclusion

In this study, we illustrate a causal modeling approach for relating

financial ratios to fundamental firm attributes and compare results to

a more traditional exploratory analysis. The use of a confirmatory

approach enables us to answer questions that are not addressed by

previous exploratory studies. Specifically, we are able to:

(1) Define and test a causal measurement model structure for a set

of financial ratios;

28

(2) Determine that the latent economic attributes of the firm are

correlated;

(3) Determine that the economic attributes are proxied quite well by

certain financial ratios; and

(4) Determine the relative degree of measurement error associated

with each individual ratio.

One of the primary benefits of a causal modeling approach is that it

allows us to determine the measurement properties of individual

accounting variables. For the most part, measurement error issues have

been ignored in selecting financial ratios or accounting variables in

various explanatory contexts. However, an understanding of the

measurement properties of accounting data appears beneficial in any

study in which the financial attributes of the firm are used as

exogenous variables.

The use of causal modeling, which is conceptually and theoretically

based, is in its infancy in accounting and there is a need for a great

deal of future research. Some suggestions for future research are

summarized below.

First, within a financial ratio context, there is a need to apply

this methodology to different time periods, different ratios, and

different samples to determine the generalizability of our results. In

this study we look at only twenty-one ratios for a manufacturing firm

sample for one year. Additional industries and additional attributes

need to be examined.

Second, measurement error is an important issue in explanatory

studies where the properties of individual model coefficients are

important. A causal modeling approach can be used to estimate the

measurement error associated with different exogenous variables. An

29

important category of explanatory studies that could potentially benefit

from a causal measurement approach are studies in which attempts are

made to link market variables to fundamental (accounting) variables.

Lev and Ohlsen [1982] call for more research of this type and causal

modeling provides an explicit approach for examining these links.*

Third, causal modeling enables one to determine the degree of

measurement error, but the issue concerning the sources of the

measurement error is not addressed. For example, we determine that

earnings per share measures profitability with a high degree of error.

However, whether the error is due to the rules for computing earnings

per share or some other sources is not addressed. Such issues would

seem to be important from both a policy and a practical point of view.

Finally, causal measurement modeling would seem to have a role in

predictive studies. While explanatory power rather than evaluation of

individual model coefficients is the main objective in such studies, the

inclusion of high measurement error variables may lead to models that

are highly sample sensitive. Research is needed to examine the effects

of measurement error in predictive studies such as bankruptcy, mergers

and acquisitions, and bond rating changes.

30

Endnotes

1. Controversy regarding the role of statistics in causal inference has

existed for some time. See Holland [1986] and Rubin [1986] for a

discussion of the propriety of causal inference in statistical analysis

and the conditions under which a causal statement can be made.

2. Mock [1976] used a measurement model perspective to suggest that

accounting data are measures of underlying unobservable constructs.

Ohlson [1979] alluded to the use of accounting numbers to represent

unobservable economic attributes of a firm in an analytic model

describing security valuation relative to the stochastic behavior of

accounting numbers. Empirical applications of a measurement model

approach are provided by Ziebart [1983], Lambert and Larcker [1985],

Ziebart [1987a], and Ziebart [1987b].

3. In the errors-in-variables problem the explanatory variable is

measured with error. The variation in the dependent variable is

explained by the square of the coefficient times the variance of the

explanatory variable and the prediction error variance. The presence of

measurement error, assumed to be independent and normally distributed,

in the explanatory variable increases the variance for the explanatory

variable and causes the coefficient to be biased downward. As the

measurement error variance increases the coefficient shrinks and becomes

less significant. Accordingly, one should choose to use financial ratio

with the smallest measurement error variance.

4. Computer programs, such as M ILS , which can handle very large data

matrices have only been made available recently.

5. The postulate of factorial causation is usually not an issue since

the measurement structure is based on a more fundamental or theoretical

system tying the observed variables to the underlying unobservable

constructs

.

6. Identification status of the model refers to the degree to which

there is enough information in the observed data relationships to solve

for the unknown parameters.

7. Note the large number of possible model configurations available for

a reasonable size data set. In this study there are 210 covariances and

the possible model configurations is a very large number.

8. For a more complete description of this estimation procedure see

Joreskog and Sorbom [1978] or Ziebart [1987a].

9. See Frecka and Hopwood [1983] for a discussion of the effects of

outliers on the distributions of financial ratios and the propriety of a

trimmed approach.

10. Details regarding the initial factor matrix, the rotated factor

matrix, and the communali ties can be obtained from the authors.

11. Given the sensitivity of the estimation algorithm to the initial

starting values, alternative starting values are introduced. The

parameter estimates are consistent and the inappropriate values are not

the result of the initial starting values.

12. For additional diagnostic assessments, the sigma (model derived

correlation) matrix, the differences between the observed correlation

matrix and the sigma matrix, and the estimated correlation matrix of all

the ratios on all of the underlying financial dimensions can be obtained

from the authors.

13. For an example of linking fundamental accounting variables to

market reactions see Ziebart [1987a] or Ziebart [1987b].

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