DECOMPOSITION ANALYSIS OF FINANCIAL STATEMENTS

MICHAEL C. WALKER, JOHN D. STOWE AND SHANE MORIARITY”

INTRODUCTION

Over the past decade there has been a resurgence of interest in financial statement analysis and a number of new techniques have been developed.’ One promising new technique, which is neither widely known among practitioners nor has been extensively investigated by academicians, is decomposition analysis. With some notable exceptions, decomposition analysis has been largely absent from the finance and accounting literature. The purpose of this paper is to reevaluate one of the suggested uses for decomposition analysis and to suggest a new application of the technique.

The first section of the paper briefly outlines the nature of decomposition analysis and summarizes the applications of the technique which have been reported in previous empirical studies. The next section reconsiders the use of decomposition analysis as a predictor of corporate bankruptcy using a different sample from those previously employed. In the final section, decomposition is proposed as a technique for monitoring the financial condition of firms. Decomposition analysis is logically suited as a monitoring device and could augment or replace traditional monitoring procedures.

PROPERTIES OF DECOMPOSITION MEASURES

Decomposition analysis is a tool normally associated with information theory. However, its use in business and economics has generally focused on the study of structural change, particularly changes over time in the relative proportions of dollar amounts in accounts or subsets of accounts. For example, the first application of decomposition analysis to financial statements was by Theil [ 121. Theil argued that decomposition could be used as a “summarizing descriptive device for changes” in the composition of firm balance sheets. Further development of the use of decomposition analysis for analyzing financial statements was undertaken by Lev [6,7,8]. Lev offered an economic rationale for the usefulness of decomposition analysis. The essence of the argument was that business organizations are homeostatic in that they seek to maintain equilibrium relationships. Any structural changes, whether planned or unplanned, are of interest to the financial analyst for identifying changes in management strategy or signaling an inability by management to maintain a desired structure. Lev [7]

*The authors are Associate Professor of Finance at North Texas State University, Assistant Professor of Finance and Associate Professor of Accounting, respectively, at the University of Oklahoma. (Paper received June 1978)

Journal of Business Finance & Accounting, 6,2(1979) 173

states that

“(Decomposition analysis) is an efficient and convenient device for identifying (a) whether significant change in financial constructs has occurred, and (b) where most of the change is located.”

Decomposition measures can be calculated for the balance sheet as a whole, the income statement, or any combination of account balances. However, three decomposition measures seem to predominate in the sparse literature on the topic. They are the balance sheet decomposition measure (BSDM), the asset decomposition measure (ADM), and the liability decomposition measure (LDM). In this paper, the calculation of these three decomposition measures will be based on the use of a balance sheet with three classes of asset and three classes of liability accounts as shown in Figure 1. Each of the six balance sheet categories is divided by twice the amount of total assets, so pij is a particular asset or liability account expressed in fractional form. The six fractions sum to unity

3 the three asset fractions sum to one-half (i pil = OS),

3 and the three liability fractions also sum to one-half ( X pi2 = 0.5).

i= 1

i= 1

The BSDM is calculated by using the fractions from two balance sheets for different points in time.

FIGURE 1 BALANCE SHEET PROPORTIONS

Assets Liabilities Quick assets PI I pl Short-term debt Inventory Pz I pz Long-term debt Long-term assets P3 1 ~3~ Net Worth

Total 1 /2 1 /2

The equation for the BSDM is

174 Michael C Walker, John D. Stowe and Shane Moriarity

where

pij

qj

= fractions from earlier balance sheet

and = fractions from later balance sheet.

When natural logarithms are used, as in this paper, the resulting measure is called a nit. The larger the BSDM, the more the structure of the balance sheet has changed between the two points in time. The BSDM will always be non-negative and indicate only the amount of change, not the direction.

Disaggregating the balance sheet into assets and liabilities, the ADM and LDM can be found by using the following equations:

and 3

LDM = Z (2qi2) Pn __ 2qi2 i = l *pi2

Again, the larger the nit, the greater the change between time points and only the amount of change is indicated. The BSDM is equal to the average of the ADM and LDM.

Some properties and uses of decomposition measures have been explored in a few empirical studies. Work in Theil [ 131 has indicated some general patterns for decomposition measures. First, LDMs are usually larger than ADMs. Second, BSDMs, ADMs and LDMs are generally larger for small firms than for large firms. Finally, these measures are generally larger for firms producing durable goods than for firms producing nondurable goods.

Two empirical studies using decomposition analysis - Lev [61 and Moyer [ 101 - have examined the usefulness of decomposition measures for predicting corporate bankruptcy. Lev found that (1) decomposition measures are generally larger for failed than for non-failed firms, (2) the LDM is generally larger than the ADM, (3) the BSDM was a better predictor of failure than the ADM or LDM, (4) the larger the time elapsed between balance sheets, the better the predictive power, and ( 5 ) the BSDM generally outperformed thirteen financial ratios when each was used as a univariate predictor of bankruptcy. The only ratio in Lev’s study that outperformed the BSDM was the ratio of cash flow to debt.

Decomposition Analysis of Financial Statements I75

Moyer used the inverse of the BSDM and the ratio of cash flow to debt in a two-variable discriminant model for predicting bankruptcy. This model was compared to the Altman model [2] and, while the two-variable model performed reasonably well, it did not match the performance of the Altman model. Moyer’s results also suggest that the ratio of cash flow to debt was a better single variable discriminator than the BSDM. The general conclusion to be drawn from these two studies is that decomposition measures have some predictive power in the area of corporate bankruptcy, but they do not measure up to a more sophisticated model.

Another potential use of decomposition measures was examined by Belkaoui [4]. Belkaoui calculated the decomposition measures for 25 Canadian companies which were taken over by other firms and compared them to the decomposition measures for a group of 25 non-acquired firms. He found that the acquired firms generally had larger decomposition measures than their non-acquired counterparts. He also reported that the BSDM had more discriminating ability than the ADM or LDM, although the difference was not large. He also found the LDMs to be larger than the ADMs.

The cumulative empirical research to date does not provide sufficient evidence to establish the utility of decomposition analysis of financial statements? The next two sections of this paper contribute additional evidence on the value of decomposition analysis. The next section reexamines the bankruptcy prediction ability of decomposition measures compared to ratios for a different sample of firms than those used by Lev and Moyer. The final section of the paper advocates a new application of decomposition measures; namely, that decomposition measures are ideally suited to monitor financial statements, that they can identify when significant overall structural changes have occurred and also can identify the sources of this change.

PREDICTION OF BANKRUPTCY

As stated above, the primary studies of decomposition analysis have been in the area of predicting corporate bankruptcy. This section follows this line of previous research and examines the usefulness of decomposition analysis for successfully classifying failed and non-failed firms in the retail and discount department store industry. The data utilized is for the 1966-1975 period and includes eight firms which failed at the end of the period and eight non-failed firms which are roughly matched in size. Using a single industry sample allows us to avoid the problems associated with inter-industry analysis. On the other hand, the small sample size precludes the use of formal statistical tests in this section.

Table 1 presents summary data on the decomposition measures for the failed

176 Michael C. Walker, John D. Stowe and Shane Moriarity

i: P

2. % 3

i: 3 r, A

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Mea

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M)

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ompo

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n 3

Mea

sure

(LD

M)

x B

alan

ce S

heet

D

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SDM

)

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v

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n M

easu

res*

fo

r Pe

rcen

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ks

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ank

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entil

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ank

Faile

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Solv

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irm

s Fi

rm in F

aile

d F

im in

Solv

ent

of M

edia

n So

lven

t

Gro

up

Gro

up

of M

edia

n Fa

iled

25%

50

%

75%

25

%

50%

75

%

21

55

164

10

30

76

30%

66

%

51

145

476

19

48

117

25%

83

%

63

146

310

20

53

89

19%

85

%

TAB

LE 2

RA

TIO

S FO

R F

AIL

ED AND

SO

LVEN

T

Rat

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or P

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ks

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d Fu

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* 2.

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8.

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9.

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10.

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11

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/NW

12

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13.

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15.

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18.

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nk of

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ian

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vent

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in Failed G

roup

75%

6.18

1.13

8.90

8.73

232

1.63

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.173

154

2.82

1.13

1.25

.074

1.07

3.23

307

.480

1.18

16.15

25%

25%

5.63

.61

4.66

7.05

1.76

1.14

.ll

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.on5

.57

.99

.43

.62

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.43

1.97

.I47

353

.270

6.32

4.66 .39

5.11

4.90

1.59

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.64

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1.85

.126

.253

.253

6.56 -

7.26

1.10

8.27

10.16

2.20

1.62

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.172

1.01

1.83

1.14

1.05

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.88

3.09

.321

503

.836

9.68

-

50%

5.30

56

6.52

6.68

1.85

1.31

.15

.019

.132

-

1.07

1.68

.55

.78

.038

.65

2.57

-198

360

Sll

11.18 -

81%

64%

35%

69%

62%

53%

52%

57%

45%

34%

36%

64%

49%

56%

42%

57%

68%

68%

5 2%

30%

50%

6.41

-89

5.78

8.14

2.02

1.37

.15

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.115

.73

1.23 .I5

31

.049

58

2.77

.268

.449

556

7.77 -

Perc

entil

e R

ank of

Med

ian

Faile

d fi

m m Solvent G

roup

17%

21%

60%

22%

35%

43%

46%

44%

62%

81%

65%

34%

57%

33%

55%

40%

44%

32%

45%

82%

*See

Tab

le 3

for

defin

ition

s of th

e m

tios

and non-failed firms for the nine time periods. The table reports decomposition measures for quartiles and the percentile rankings for median failed and non-failed firms in the opposite category. Our results, to a great extent, parallel the findings of Lev [6] . We also find that the LDM is generally larger than the ADM and that the three decomposition measures are generally larger for failed than non-failed firms. However, the discriminating power of the BSDM is not overwhelming. For example, the BSDM of the median solvent firm is in the 19th percentile of the failed group and the BSDM for the median failed firm is in the 85th percentile of the solvent group. The discriminating power of the LDM is slightly less than that of the BSDM and both are apparently superior to the ADM.

Table 2 presents data an the ability of financial ratios to discriminate bankrupt from non-bankrupt firms. Table 2 shows the values of 20 ratios for failed and non-failed firms and the percentile rank of failed and non-failed firms in the opposite category. The ratios are defined in Table 3. Two of the ratios - S/I and CL/NW - appear to have approximately the same classification power as the

TABLE 3

DEFINITIONS OF RATIOS USED

1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

S/I

S / N W s/wc I/WC NI/wc MIS

CL/NW TD/NW LTD/WC CL/I NI/TA QA/CL S/TA LTD/TA NW/TA LTD/NW S/FA

FA/NW

CA/CL

SaleslInventory Fixed Assets/Net Worth SaleslNet Worth SaleslNet Worlung Capital Current AssetslCurrent liabilities Inventory/Net Worlung Capital Net Income/Net Working Capital Net Income/Sales Net Income/Net Worth Current Liabilities/Net Worth Tot a1 Debt /Ne t Worth Long Term Debt/Net Working Capital Current Liabilities/Inventory Net Income/Total Assets Quick Assets/Current Liabilities SaleslTotal Assets Long Term DebtlTotal Assets Net Worth/Total Assets Long Term DebtlNet Worth Sales/Fixed Assets

BSDM and LDM. The ADM appears to achieve discrimination only about as well as the average ratio. Of course, other ratios which we did not use which include

Decomposition Analysis of Financial Statements 179

additional data might prove to do as well or better than the decomposition measures. For example, both Lev [6] and Moyer [lo] found cash flow to debt to be superior to the BSDM, and Lev found the cash flow to sales to be approximately equal to the BSDM in predictive power.

When the nine year period is divided into shorter intervals, we find that both the decomposition measures and the ratios discriminate better between the failed and non-failed firms in the last three years prior to bankruptcy. The LDM and BSDM discriminate fairly well in the last three years, although six of the ratios have the same 0 1 better discriminatory ability. (The six ratios were FA/hW, NIIWC, NI/S, NI/NW, NI/TA, and NWITA.) Interestingly, the ADM had practically no ability to discriminate between the failed and non-failed firms in our sample, it was weaker during the last three years than seventeen of the twenty ratios. For longer periods prior to bankruptcy, the discriminating ability of the decomposition measures and ratios generally diminished rapidly. The BSDM, however, still discriminated fairly well four to six years prior to bankruptcy, but the LDM had no value during this period.

To summarize the bankruptcy prediction results, we have observed several previously reported relationships in our sample: (1) decomposition measures are generally larger for failing firms, (2) the liability decomposition measure is generally larger than the asset decomposition measure, and (3) the decomposition measures have about the same bankruptcy prediction power as a good ratio. However, we do find one difference. Lev [6] found the ADM and LDM to have almost the same discriminating ability between bankrupt and solvent firms; we found the ADM to have very little ability to do this.

MONITORING FINANCIAL STATEMENTS

In this section we argue that decomposition measures are well suited for monitoring financial statements in search of significant structural changes in a firm’s financial condition. If a decomposition measure is small, we know that the composition of the financial statement between two points in time is substantially unchanged. If, in addition, we had analyzed the first financial statement, then it follows that the analysis of the second financial statement would probably be a waste of resources. Conversely, a large DM indicates that the composition of the financial statement has changed significantly. In this case it is likely that the second statement should be evaluated further. In addition to the a priori argument that DMs identify structural changes, we also discuss the correlations between DMs and changes in financial ratios and the correlations between DMs and changes in linear combinations of ratios. From the correlation results, we further argue that decomposition techniques can complement or replace some traditional methods of monitoring financial statements.

180 Michael C Walker, John D. Stowe and S h n e Moriarity

While we know that DMs indicate whether the structure of a firm’s financial statement has changed, we are not convinced that DMs provide a measure of a firm’s financial condition. In our discussion in the previous section - and in the Lev and Moyer papers - high DMs were associated with bankruptcy, which implies that large structural changes are bad and that small changes are good. But this conclusion is unlikely to be universally correct. For a large structural change in a firm can be associated both with a significant deterioration and a significant improvement in financial position. This observation would be consistent with several examples in our sample where large structural changes (and high DMs) were associated with firms which remained solvent. It is not surprising that decomposition measures are high when a firm is going through the wrenching restructuring prior t o bankruptcy. That is, bankruptcy may imply h g h BSDMs, but not the reverse; high BSDMs do not necessarily imply bankruptcy. Decomposition measures identify that a structural change has occurred, but the implicit presumption in the bankruptcy research that change (high DMs) must have a negative valence may be an incorrect assumption.

The relationship between DMs and other decisions such as loan credit-worthiness, the riskiness of stock, or bond ratings, may be just as clouded. Importantly though, once a judgement on these issues is formed, the DMs will indicate if the balance sheet changes significantly. If the balance sheet of a firm does change, then that firm should be re-examined to see if credit-worthiness (or some other characteristic) has improved or deteriorated from the previously held opinion. In other words, decomposition measures may not be valuable as an index of financial condition, but they are a measure of the amount of change in the structure of financial statements.

The relationship between decomposition measures and changes in ratios provides further insight into why decomposition measures are measures of change and not measures of financial condition. The first three columns of Table 4 contain the Spearman rank correlations between the ADM, LDM, or BSDM and the changes in the values of twenty ratios for the sixteen firms in the bankruptcy study. These three columns reveal that the decomposition measures are generally uncorrelated to the change in a ratio. In contrast, the last three columns of Table 4 present the Spearman rank correlations between the three decomposition measures and the absolute values of the changes in ratios. Now the decomposition measures are generally significantly related to the absolute values of the amount of change in a ratio. This finding supports our a prion arguement that decomposition measures indicate that a change has occurred, but that one should not assign a valence (or value judgement) to the change.

Discriminant models are widely used to evaluate loans, predict bankruptcy, and estimate the riskiness of bonds. Presumably then, discriminant models could also be used to monitor changes in financial statements. Because the discriminant

Decomposition Analysis of Financial Statements 181

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Rat

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3 .0

2 .04

-.01

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-.0

5 .06

.02

-.13

-.04 .I1

LDM

-.16

-.03

-.11

-.34 .07

-.16

-.14

-.09

-.13

-.oa .07 .oo

-.11

-.16 .07

-.09 .02

-.19 .04

.01

BSD

M

-.19 .01

-.06

-.27 .04

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BSDM

.39

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21

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scores in these models are frequently linear combinations of financial ratios, decomposition measures will generally be highly correlated to absolute values of changes in discriminant scores because the DMs are highly correlated to the absolute values of changes in the ratios themselves.‘ Thus, high decomposition measures will be associated with a significant increase or decrease in a firm’s discriminant score and we are forced to conclude that if reliable discriminant models are in use, the use of decomposition measures would be redundant. However, because legitimate statistical and economic questions exist about 1) the sample used to construct discriminant models, 2) the stationarity of the variables and coefficients of the models, and 3) the homogeneity of the firms being scored, users of discriminant models might still want to augment their analysis with decomposition analysis. Decomposition analysis, since it is not a statistical procedure, avoids the statistical problems of discriminant models.

To a current user of discriminant models, the calculation of decomposition measures would be almost costless. In those situations were discriminant models are impracticable or unreliable, decomposition analysis can still report structural changes in the financial information about firms. Much like discriminant analysis, decomposition analysis may help a bank allocate scarce loan evaluation resources and, perhaps, improve the quality of the loan review process. Decomposition analysis may not be useful for making the initial evaluation, but it may be an excellent device to monitor customers to see when a reevaluation is justified. We now suggest a monitoring procedure.

In order to determine if a significant change has occurred and to locate the specific sources of the change, a bank or business monitoring financial statements might consider a process as follows:

(1) Calculate BSDMs on all balance sheets as soon as received. If a firm’s BSDM is below some threshold value, the balance sheet has not changed significantly and would not possess sufficient information to justify reevaluating that firm. However, if the BSDM exceeds the threshold, the firm should be analyzed further.

(2) changed significantly.

(3) Examine the components of the decomposition measures to see which balance sheet items have changed significantly, and direct further analysis to those areas.s

Look at the ADM and the LDM to see which side(s) of the balance sheet

The desirability of such a process of monitoring financial statements depends, of course, on whether it possesses some predictive advantage over alternative techniques or it reduces the cost of monitoring financial statements. This is an empirical question which depends on the situation of the user. In addition, the bank or

Decomposition Analysis of Rlnancial Statements 183

business might use multiple-year decomposition measures and income statement decomposition measures. Decomposition measures spanning several periods could be used as well as single-period decomposition measures. Several periods of gradual change in the same direction would result in low single-period DMs, but the cumulative change found with a multiple-period decomposition measure could be significant.

The discussion in this paper has been confined to balance sheet decomposition measures, but it would also be easy to construct income statement decomposition measures to use in conjunction with BSDMs. One drawback of decomposition measures is that they do not permit the calculation of measures when a component (such as net worth on a balance sheet or net income on an income statement) is negative because the logarithm of a negative number is undefined. Of course, this would occur more frequently with income statements than with balance sheets.

SUMMARY

Decomposition measures may prove to be useful information for financial statement analysis. Previous empirical research on DMs has been descriptive or shown how DMs may be used to predict bankruptcy or takeovers. Our sample of retail department and discount stores exhibited substantially the same descriptive and predictive characteristics as this previous research.

No previous research has been published on the relationships between DMs and changes in ratios or changes in linear combinations of ratios. We find significant correlations here which suggest that decomposition analysis would be a useful adjunct to, or replacement for, other techniques of monitoring financial statements. When monitoring financial statements with decomposition measures, significant overall structural changes in financial data will be detected by the decomposition measures; the components of the decomposition measures are able to direct attention to the components of the financial statements which have changed in much the same manner that traditional ratios do. Decomposition analysis may have its greatest value as a monitoring device and our results indicate that this application merits additional attention.

NOTES

Some of the significant developments in financial statement analysis include 1 ) the use of univariate statistics to validate the use of ratios for predicting corporate bankruptcy (e.g., Beaver’s examination of ratios as predictors of bankruptcy (3) ) , 2) the use of multivariate statistics to predict events (e.g., Altman’s use of multiple discriminant analysis to predict fum insolvency (2)), 3) the use of factor analysis to select variables for use in further analysis (e.g., Pinches and Mingo’s use of factor analysis to choose variables for use in a multiple discriminant analysis model for predicting bond ratings (1 1 ) ), 4) the inclusion of new types of variables such as the slope of the trend line for

184 Michael C Walker, John D. Stowe and Shane Moriarity

a ratio, the deviation from a trend line, and the coefficient of variation of a ratio along with ratios in multivariate statistical models (e.g., Meyer and Pifer’s use of 0-1 regression to predict bank failure (9) 1, 5 ) the use of factor scores of ratios instead of specific ratios as variables in a multiple discriminant analysis model, and (6) the use of information theory concepts to predict corporate bankruptcy (e.g., Lev‘s use of decomposition analysis (6) 1.

While he did not use decomposition measures to reflect changes in financial statements, Abdel-khalik (1) designed an experiment to test whether the entropy of financial

’ statements n

(H =. p. lnp) 1=1 I

was correlated to the subjective risk estimates of a number of bank loan officers. Entropy is inversely related to the level of aggregation in a financial statement. He found that entropy (aggregation) was uncorrelated to the bank loan officer evaluation. Abdel-khalik is dubious of the relevance of entropy for decision making. While they do not provide any empirical evidence, Horowitz and Horowitz ( 5 ) also object t o using entropy as a measure of the amount of information in a financial statement.

The means of the decomposition measures are not presented in the table because the means are distorted by a few extreme values. The mean BSDM, AqM and LDM respectively for the solvent group were 175, 132, and 218 (in 10- nits). For the failed group they were 576,238, and 904, respectively. Note that the mean BSDMs equal the average of the mean ADMs and LDMs. Such is not the case for the median values for BSDM, ADM and LDM. The BSDM would approach the average of the ADM and LDM for a given percentile only if ADM and LDM were highly correlated. In this case they are not; the Spearman rank correlation coefficient for ADM and LDM is only .29. Of course each is more correlated with BSDM achieving a coefficient of .62 and .87 for ADM and LDM, respectively.

The authors constructed several ad hoc indices of linear combinations of variables similar to the Altman bankruptcy model, and to credit-scoring (short term) models. Our sample is too small to construct a discriminant model. The relationship between the DMs and the indices is similar to the relationship between DMs and the individual ratios in Table 4. The DMs were not significantly correlated to the changes in the indices, but they were highly correlated to the absolute values of the changes in the indices.

The authors estimated correlations between each of the twenty ratios employed in the paper and each of the six components of the BSDM. The ratios were highly correlated to at least one DM component. Thus, the DM compoxnts would indicate the same sources of change that could be found with financial ratios.

’

‘

’

REFERENCES

(1) A. Rashad Abdelkhalik, ‘The Entropy Law, Accounting Data and Relevance to to Decisionmaking”, The AccountingReview, April 1974, pp. 271-283.

Edward I. Altman, “Financial Ratios, Discriminant Analysis, and the Prediction of Corporate Bankruptcy”, Journal of Finance, September 1968, pp. 589-610.

William H. Beaver, “Financial Ratios as Predictors of Failure”, Empiricul Reseurch in Accounting Selected Studies, 1966, Supplement to Volume 4, Journal of Accounting Research, pp. 71 - 127.

(2)

(3)

Decomposition Analysis of binancia1 Statements 185

(4) Ahmed Belkaoui, “The Entropy Law, Information Decomposition Measures and Corporate Takeover”, Journal of Business Finance and Accounting, Fall 1976, pp. 41-52.

(5) Ann R. Horowitz and Ira Horowitz, “The Real and Illusory Virtues of Entropy- based Measures for Business and Economic Analysis”, Decision Sciences, January 1976, pp. 121-136.

Baruch Lev, “Financial Failure and Informational Decomposition Measures”, Accounting in Perspective: Contributions to Accounting Thought by Other Disciplines, R.R. Sterling and W.F. Bentz, eds. (Cincinnati, Southwestern Publishing Company,

(6)

1971), pp. 102-111.

(7) Baruch Lev, “Decomposition Measures for Financial Analysis”, Financial Management, Spring 1973, pp. 56-63.

(8) Baruch Lev, FinancLI Statement Analysis, (Englewood Cliffs, N.J. : Prentice-Hall, Inc.), 1974, Chapter 4.

Paul A. Meyer and Howard W. Pifer, “Prediction of Bank Failures”, Journal of Finance, September 1970, pp. 853-868.

R. Charles Moyer, “Forecasting Financial Failure: A Reexamination”, Financirrl Management, ping 1977, pp. 11-17.

(1 1) George E. Pinches and Kent A. Mingo, “A Multivariate Analysis of Industrial Bond Ratings”, Journal of Finance, March 1973, pp. 1-18.

Henri Theil, “On the Use of Information Theory Concepts in the Analysis of Financial Statements”, Management Science, May 1969, pp. 459-480.

Henri Theil, Statistical Decomposition Analysis: With Applications in the Social and Administrative Sciences (Amsterdam, Holland: North-Holland Publishing Company), 1972.

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186 Michael C. Walker, John D. Stowe and Shane Moriarity