Classifying the stability scores of the big-three American automotive companies using DEA window analysis.

Alshare, Khaled ; Luo, Xueming ; Mesak, Hani I. 等

ABSTRACT

This paper evaluates the stability of the efficiency scores of the three largest American automotive companies over three 4-year windows (1986-1989, 1990-1993, and 1994-1997). The study employs a nonparametric technique called Data Envelopment Analysis (DEA), in particular DEA window analysis, to evaluate the stability of the companies' efficiency. The automotive firms are classified based on their stability scores, using cluster analysis into four groups: efficient stable, efficient unstable, inefficient unstable, and inefficient stable. The results of two DEA models (CCR and BCC) are consistent to a great extent in classifying the firms over the three 4-year windows. Both models indicate that, for the studied period, Ford Motor Company is classified by both DEA models 92% (22/24) of the time as either efficient stable or efficient unstable. Chrysler Corporation is classified 71% (17/24) of the time as efficient stable or efficient unstable. On the other hand, General Motors Company is classified 67% (16/24) as efficient stable or efficient unstable. The empirical results reveal that each company could have reduced advertising spending, total assets and number of employees while maintaining sales volume and market share during the period.

BACKGROUND

The efficiency in the auto manufacturing industry has been, over the last decade, analyzed in two major studies (Womack, Jones, and Roos, 1990; Fuss and Waverman, 1993). However, there are not many articles that have addressed the efficiency performance of the U.S. big-three auto companies using Data Envelopment Analysis (DEA). To fill this void, this paper is intended to evaluate and analyze the stability of the efficiency of U.S. automotive companies during the period 1986-1997. DEA is used to measure efficiency when there are multiple inputs and outputs and there are not generally accepted weight for aggregating inputs and aggregating outputs. The present study has a significant marketing orientation in the sense that most of the considered inputs and outputs are basically measures of marketing phenomena. In the marketing literature, a number of scholars applied DEA in order to gauge and analyze efficiency. Notable examples include the study of Charnes et al. (1985), who have first discussed potential applications of DEA in retailing and sales research. Metzger (1993) presented DEA methods in measuring the effects of appraisal and prevention costs on productivity. Chebat et al. (1994) used DEA to assess the degree to which allocation of marketing resources affects the corporate profits of Canadian firms. Boles, Donthu, and Ritu (1995) proposed DEA to evaluate salesperson performance. Horsky and Nelson (1996) evaluated and benchmarked the salesforce size and productivity by using DEA. Donthu and Yoo (1998) utilized DEA to assess the productivity of 200 retail stores. Thomas et al. (1998) evaluated the efficiency of 552 individual stores for a multi-store, multi-market retailer using DEA. Pilling, Donthu, and Henson (1999) employed DEA to adjust sales performance by territory characteristic, derived from the Census of Retail Trade. The above review reveals the absence of advertising applications from the literature. Although a number of authors (e.g., Asker and Carman 1982; Tull et al. 1986) have examined the issue of advertising efficiency within the context of a single firm, there has not been work involving studying the relative efficiency of advertising spending of competing firms in the same industry. DEA can be instrumental in achieving such a goal. DEA is intended to measure the relative efficiencies among DMUs (Decision Making Units) and enables direct measurements of efficiency. DEA formulates a series of linear programming models, one for each DMU. These models can identify the relatively efficient DMUs and accord them a rating of value one, or 100% efficiency. The major advantages of DEA over traditional ratio and regression approaches include (1) DEA doesn't require a knowledge of a production function linking input variables with output variables; (2) In DEA, there is no need to assign rigid weights to inputs or outputs; and (3) DEA offers management a variety of useful insights including relative productivity scales and efficiency gaps within different inputs and outputs that help in indicating causes for inefficiency (Charnes et al. 1994). The most important consideration in any DEA application is the selection of model specification including input and output variables. Regression analysis can empirically infer at least potential input/output relationships, while DEA only presumes that such relationships exist. Researchers, therefore, must make sure that 1) outputs are statistically related to inputs, 2) the variables represent management overall goals and policies, and 3) the appropriate model is used. Also considerable effort should be spent in selecting the number of comparable DMUs to include in the analysis. The number of DMUs to consider in the analysis is a controversial issue. While Ali et al. (1988) and Banker and Maindiratta (1986) recommend that in traditional DEA the number of units should be at least twice the sum of the inputs and outputs, Golany and Roll (1989) warn that the larger the number of units in the analysis set, the lower the homogeneity within the set and thus increasing the possibility that the results may be affected by some exogenous factors which are not of interest. For example, small assembling automobile firms would not be meaningful when compared with the big-three companies in the United States. In the automotive and airplane manufacturing industries, a few large companies dominate the market. In this situation, DEA window analysis becomes more appropriate. DEA window analysis is used to track the efficiency over time. It pools the observations of several consecutive years (e.g., 4 years) as an 4-year window. It then reveals the efficient DMUs in this 4-year period by using DEA models. Thus the efficient DMU denotes the best performance in the 4-year period (Thore et al., 1996). One of the limitations of DEA is that it measures the technical efficiency (optimizing the use of resources), leaving out the allocation efficiency (allocating the available resources). Moreover, DEA is very sensitive to outliers, which make the selection of DMUs critical. Outliers may greatly affect the shape of the efficient frontier and alter the efficiency estimates (Donthu and Yoo, 1998). In addition, self-identifier and near-self-identifier problems may also arise (Bauer et al. 1998). That is, some DMU may be self-identified as 100% efficient not because they dominate any other DMUs, but because no other DMUs or linear combination of DMUs are comparable in the model. However, in recent years, many researchers have focused on DEA sensitivity analysis aspects (Charnes, Rousseau, and Semple, 1996; Seiford and Zhu, 1998; Zhu, 2001). The use of sensitivity and stability analyses of efficiency scores of DEA models should make decision makers more confident in the DEA results.

RESEARCH FRAMEWORK

The research framework for this study is depicted in Figure 1. The research framework consists of the following steps:

a) The Cobb-Douglas Production Function is used to assess the relationship between input and output variables.

b) DEA window sensitivity analysis is performed to obtain the stability scores for each company.

c) Cluster analysis is used to classify the automotive firms based on their stability scores into Efficient Stable (ES), Efficient Unstable (EUS), Inefficient Unstable (IUS), and Inefficient Stable (IES) classes.

d) Statistical tests are used to test for significant correlations between the results of the two DEA models (CCR vs. BCC), and the significance of any observed disagreements in efficiency classifications.

[FIGURE 1 OMITTED]

A. The Cobb-Douglas Production Function

The rationale of our approach relies upon the macroeconomic production model. The Cobb-Douglas production function has been extensively applied to evaluate firm performance from the productivity point of view (Allison and English, 1993). The Cobb- Douglas function may be formulated as follows.

Y = K CA LB

where

Y = the output,

C = the capital inputs,

L = the labor inputs,

A = the elasticity coefficient of capital inputs,

B = the elasticity coefficient of labor inputs, and

K = scaling constant.

Comparable to the Cobb-Douglas function, this paper uses the following indicators for inputs: total assets (in billions of USD), number of employees (in thousands), and advertising expenditures (in millions of USD). The outputs consist of net sales ([Y.sub.1]) (in billions of USD), and market share ([Y.sub.2]) (in percentage of the U.S. market). Thus the Cobb-Douglas function is modified to take on the following form:

Yi = eK * ADVETA * TOTASB * EMPLOYC, i = 1, 2. (1)

Observe that equation (1) is a non-linear model. It needs to be linearized before using the Ordinary Least Squares (OLS) procedure for its estimation. Taking the natural logarithm of both sides of (1) produces:

Ln[Y.sub.i] = K + A . Ln (ADVET) + B . Ln (TOTAS) + C . Ln (EMPLOY), i = 1,2. (2)

Where

ADVET = observation of input of advertising spending,

TOTAS = observation of input of total assets,

EMPLOY = observation of input of employees,

A = elasticity coefficient of advertising,

B = elasticity coefficient of total assets,

C = elasticity coefficient of employees, and

K = scaling constant.

Equation (2) presents a model of decreasing returns to scale for increased total assets, advertising spending, and number of employees. The model allows for interaction effects and the coefficients can be interpreted as elasticities. Equation (2) also assumes for simplicity that each input (expressed in terms of its natural logarithm), considered separately, has the same effectiveness on a given output (expressed in terms of its natural logarithm) across the three manufacturers.

B. DEA Window Analysis

Since we have only three DMUs (three companies) each year, three 4-year windows analysis were conducted to get the efficiency scores for DMUs during each 4-year window (3*4 = 12 DMUs). The rationale for dividing into four-year periods is that a product cycle in the automotive industry lasts about four years. Each generation for a specific car brand, with a few exceptions, is held approximately four years before being supplanted by the next generation, given the fierce competition and quickly updating technology in the industry (Fuss and Waverman, 1993). It is recommended to start the analysis by using the original DEA model (CCR) introduced by Charnes, Cooper, and Rohdes (1978) because it reveals the differences among the DMUs in the most unforgiving manner (e.g., it has the largest reference set). The results of the BCC model, which was introduced by Banker, Charnes, and Cooper (1984), are also compared with the results of the CCR model in this study. Therefore, two DEA models (CCR and BCC) input oriented formulations are used to evaluate the stability classification of the efficiency of the three companies.

C. DEA Sensitivity Analysis

For each company, the sensitivity measure or stability percentage ([alpha]) is calculated by solving certain linear programming problems developed by Charnes, Rousseau, and Semple (1996). This particular linear programming formulation calculates a, the percentage radius of change in the input-output space within which a DMU's classification remains unchanged. It should be noted that a positive value of a means that the DMU is an efficient one, while a negative value means that the unit is inefficient. On the other hand, the absolute value of [alpha] is the percentage within which the DMU's Classification remains unchanged.

D. Cluster Analysis

For each separate group (efficient and inefficient), univariate cluster analysis is performed on the absolute values of the stability scores ([alpha]) to create stable and unstable categories. The stable group has high absolute value of a and the unstable group has low absolute value of [alpha]. Thus, resulting in four final classifications; Efficient Stable (ES); Efficient Unstable (EUS); Inefficient Unstable (IEUS) and Inefficient Stable (IES).

E. Statistical Tests

Since each automotive firm is categorized as efficient stable, efficient unstable, inefficient unstable, or inefficient stable under each DEA model (CCR and BCC), several nonparametric procedures could be used to test the significance of any observed disagreement in efficiency classifications. One test is the Friedman test for dependent samples with classes ranked as: ES=4, EUS=3, IEUS=2, and IES=1. In addition to that test, Spearman Correlation coefficient could be used to test for significant correlations between the stability scores related to the two DEA models.

DATA COLLECTION

Standard and Poor's Compustat database was the source for the financial data related to companies net sales, total assets, and number of employees. Advertising Age was the source for the advertising expenditures from 1986 to 1997. The market share data was obtained from Ward's Auto World databank.

EMPIRICAL RESULTS

This section reports the results of estimating the Cobb-Douglas production function in assessing the relationship between the input and the output variables. It also reports the results of the analysis of the stability scores for the automotive companies over the three 4-year windows.

The Cobb-Douglas Production Function Estimation Results

Although it is always better to estimate the sales volume and market share equations jointly using the method of seemingly unrelated regression, SUR, (Zellner, 1962) there are circumstances when it is just as good to estimate each equation separately. One of such circumstances is actually in conformity with our situation. Indeed, some advanced algebra is needed to prove that OLS and SUR give identical estimates when the same explanatory variables appear in each equation (Hill, Griffiths, and Judge, 1997). Therefore, the two equations related to sales volume and market share for the U.S. automotive industry would be estimated separately using OLS.

After adding error terms and applying White's procedure for heteroskedasticity correction, Table 1 displays the regression results of equations (2). The results show that the sales volume is statistically related to the input variables (total assets, advertising expense and number of employees). The regression model (dependent variable = sales volume) has an F- statistic of 274.50, with p-value less than 0.001, and an adjusted R-square of about 0.96. All the input explanatory variables' standardized coefficients (e.g. advertising, employees, and total assets) are significantly different from zero with t-statistic of p-value less than 0.01. Also the F- statistic for the regression model (dependent variable = market share) is 79.65, with p-value less than 0.001, and adjusted R-square of about 0.89. Again, the market share output is statistically related to advertising (p-value less than 0.05), total assets (p-value less than 0.10), and employees (p-value less than 0.01).

The small values of variance inflation factors (VIF's) shown in Table 1, suggest that multicllinearity is not an issue in any of the models (Neter, Wasserman, and Kutner, 1990). Furthermore, there is no evidence of the presence of serial correlation in any of the models (Durbin and Watson, 1951) adding more credence to the robustness of the model. The inputs and outputs variables used are statistically related, thus satisfying the variable requirements of DEA applications (Golany and Roll, 1989). The DEA results are reported next.

Comparing Companies over Three Four- Year Windows

The performance of each manufacturer is examined for three 4-year window periods. The performance of each company during 1994-1997,1990-1993, and 1986-1989 are compared. In conducting such analysis related to each window, a certain company in a particular year is considered as a separate DMU by itself. The linear programming problems (see Charnes, Rousseau, and Semple, 1996) are applied for the entire 4-year window, one at a time for each DMU, resulting in obtaining the stability scores for a total of 12 DMUs. The stability analyses of these three four-year windows are summarized in Table 2. Most of the Chrysler and Ford's years are efficient unstable (for both BCC and CCR models). On the other hand, most General Motors' years (6/12) are inefficient-unstable from the CCR model results, and (9/12) are efficient unstable from the BCC model results. It is worth mentioning that other 4-year windows results (1993-1996, 1992-1995, 1991-1994, etc.) arrive at similar conclusions to those related to the above three 4-year windows.

Table 3, derived from Table 2, shows the number of efficient years during each 4-year window for both DEA models. GM received the least number of efficient years (16/24). This suggests that GM is the least efficient manufacturer compared to the other two competitors. On the other extreme, Ford enjoyed the largest number of efficient years during the three 4-year windows (22/24). Chrysler received (17/24) as efficient. It should be noted that none of the three companies is classified as inefficient stable in the three 4-year windows analysis

The correlations between the stability scores of the two models (CCR and BCC) for each one of the three 4-years windows are significant as shown in Table 4. One can say that the results of the two DEA models are in agreement to a great extent with respect to the automotive firms' stability scores. It should be noted that when the stability scores for the three 4-year windows are pooled together, the correlation between the two models was also significant (Spearman's correlation coefficient r = 0.679; p-value = 0.000005).

The Friedman test (for ordered classes) is employed using the data depicted in Table 2 to test the hypothesis of no difference in efficiency classifications (ES, EUS, IEUS, and IES) between the two DEA models. The results of the Friedman test for two of the three 4-year windows are significant (p-value = 0.0254; p-value = 0.0832 for window 90-93 and window 86-89, respectively), indicating that the observed efficiency classifications are significantly different between the two DEA models for these two windows. The result of the Friedman test for the third 4-year window (94 - 97 window) is not significant, indicating that the observed efficiency classifications are not significantly different between the two DEA models for that window. These findings imply that DMUs classification results obtained from the two DEA models become more consistent with one another upon using the stability score as an additional dimension for classification. It is known from the literature that when the efficiency score is used as the sole classification dimension, the CCR model generates fewer efficient DMUs than the BBC model does.

IMPILICATIONS AND CONCLUSIONS

This study employs two DEA models in conjunction with cluster analysis in order to classifying stability scores of the U.S. big-three auto companies. The results of both models (CCR and BCC) indicate that Ford was the most efficient leader during each consecutive four-year period, or product cycle. General Motors was the most inefficient company in the industry. Chrysler is positioned to lie between these two extremes. These findings are consistent with the point of view of industry experts (e.g., Vasilash, 1996 and Valsic, Naughton, and Kerwin, 1998).

Implications for Management

The authors are fully aware that the results of this study will be welcomed by the manufacturer placed first (Ford) and disregarded by the one placed last (General Motors). The worst performer will question these efficiency estimates by arguing that important inputs and/or outputs have not been incorporated in the analysis, or that the DEA CCR and BCC models utilized in deriving the conclusions come into question. The best performer, on the other hand, will be sufficiently satisfied without bothering about these shortcomings. However, DEA results are descriptive (diagnostic) in nature rather than perspective. Thus, management should examine in depth the results of DEA models in order to make appropriate corrective decisions. For example, efficiency scores and slack variables obtained through solving the original DEA models, reveal that each company could have reduced advertising spending, total assets and number of employees while maintaining sales volume and market share during the studied period. A viable way to reduce waste in advertising spending is to adequately test ad campaigns that are already running. Strategies for dealing with excess capacity includes better production planning and control processes, reviewing the level of product variety in the face of conflicting cost and revenue implications, and selling money-losing businesses. A common strategy to deal with a surplus of employees is laying some of them off. By working closely with the United Auto workers to avoid potential strikes, the side-effects of such action can be minimized.

The additional classification of DMUs into stable or unstable status would allow management to have more confidence in their conclusions about the performance of the DMUs. As a result, management should seek and retain efficient stable DMUs and avoid or change the situation of inefficient stable ones. Management should also carefully monitor efficient unstable DMUs and take appropriate measures to keep them efficient. On the othert hand, management may adopt radical changes with respect to inefficient unstable DMUs. For example, in the summer of 1998, General Motors swapped brand-based operating divisions for a centralized marketing organization supported by a new field sales and marketing system to boost efficiency.

Implications for Researchers

Since there are not many studies that have evaluated the efficiency performance of the U.S. big-three auto companies using DEA technique, this study has intensively employed DEA sensitivity analysis in classifying the stability scores of the big-three auto companies in the U.S. Its major contribution is that it provides a post analysis for DEA results. Many researchers have employed DEA models in many applications; however, they have used only efficiency scores to draw their conclusions. This study does not only use efficiency scores in drawing its conclusions, but also calculates stability scores, which provide investigators with information on how efficiency scores are robust to any changes in the values of inputs or outputs. In addition, this study employs cluster analysis to classify DMUs into four distinct groups: Efficient Stable (ES), Efficient Unstable (EUS), Inefficient Unstable (IEUS), and Inefficient Stable (IES) in order to provide management with reliable conclusions. One direction for future research is to compare U.S. auto companies to its counterparts in other countries such as Japan and Europe. Another direction would be to examine the efficiency of brands within the three companies. A third plausible direction for future research would be to compare DEA results with other traditional methods of evaluating efficiency such as ratio analysis and production functions.

REFERENCES

Ali, I., Charnes, A., Cooper, W., Divine, D., Klopp, G., & Stutz, J. (1988). An application of Data Envelopment Analysis to us army recruitment districts. Application of Management Science Research and Analysis (Edited by Shutz, R. L.), JAI Press.

Allision, J. & English, J. (1993). The behavioral economics of production. Journal of the Experimental Analysis of Behavior 60, 559-569.

Asker, D., & Carman, J. (1982). Are you over advertising? Journal of Adversising Research, 22 (August-Sptember), 57-70.

Banker, R., Charnes, A., & Cooper, W. (1984). Some models for estimating technical and scale inefficiencies in Data Envelopment Analysis. Management Science, 30, 1078-1092.

Banker, R., & Maindiratta, A. (1986). Piecewise loglinear estimation of efficient production surfaces. Management Science, 32(1), 126-135.

Bauer, P., Berger, A., Ferrier, G., & Humphrey, D. (1998). Consistency conditions for regulatory analysis of financial institutions: A comparison of frontier efficiency methods. Journal of Economics and Business, 50, 85-114.

Boles, J., Donthu, N., & Ritu, L. (1995). Salesperson evaluation using relative performance efficiency: the application of Data Envelopment Analysis. Journal of Personal Selling and Sales Management. 15 (3), 38-49.

Charnes A., Cooper, W., & Rhodes, E. (1978). Measuring the efficiency of Decision Making Units. European Journal of Operational Research, 3,429-444.

Charnes, A., Cooper, W., Learner, D., & Philips, F. (1985). Management science and marketing management. Journal of Marketing, 49(Spring), 93-105.

Charnes A., Cooper, W. , Lewin, A., & Seiford, L. (1994). Data Envelopment Analysis: Theory, methodology, and applications, Kluwer Academic Publishers,

Charnes, A., Rousseau, J., & Semple, J. (1996). Sensitivity and stability of classifications in Data Envelopment Analysis. The Journal of Productivity Analysis, 7, 5-18.

Chebat, J, Pierre, F., Arnon, K., & Tal, S. (1994). Strategic auditing of human and financial resource allocation in marketing: An empirical study using Data Envelopment Analysis. Journal of Business Research, 31, 197-208.

Donthu, N., & Yoo, B. (1998). Retail productivity assessment: using Data Envelopment Analysis. Journal of Retailing, 74 (1), 89-117.

Durbin, J., & Watson, G. (1951). Testing for serial correlation in least squares regression II. Biometrika; 38, 159-178.

Fuss, M., & Waverman, L. (1993). Costs and Productivity in Automobile Production: The Challenge of Japanese efficiency, Cambridge University Press, Cambridge.

Golany, B., & Roll, Y (1989). An application procedure for DEA, OMEGA: International Journal of Management Science, I7 (3),237-250.

Hill, C., Griffiths, W., & Judge, G. (1997). Undergraduate Econometrics, John Wiley & Sons, Inc., New York.

Horsky, D., & Nelson, P. (1996). Evaluation of sales force size and productivity through efficient frontier bench marketing. Marketing Science, 15 (4), 301-320.

Metzger, L. (1993). Measuring Quality Cost Effects on Productivity Using Data Envelopment Analysis. Journal of Applied Business Research, 19, 369-379.

Neter, J., Wasserman, W., & Kutner, M. (1990). Applied linear statistical models, 3rd ed., Irwin, Homewood, IL

Pilling, K., Donthu, N., & Henson, S. (1999). Accounting for the impact of territory characteristics on sales performance:

Relative efficiency as a measure of salesperson performance. Journal of Personal Selling and Sales Management, 19 (2), 35-45.

Seiford, L. & Zhu, J. (1998). Theory and methodology stability regions for maintaining efficiency in Data Envelopment Analysis. European Journal of Operational Research. 108, 127 139.

Thomas, R., Barr, R., Cron, W., & Slocum, J. Jr. (1998). A process for evaluating retail store efficiency: a restricted DEA approach. International Journal of Research in Marketing, 15 (5), 487-501.

Thore, S., Phillips, F., Ruefli, T., & Yue, P. (1996). DEA and the management of the product cycle: The U.S. computer industry, Computers & Operations Research, 23 (4),341-357.

Tull, D., Wood, V., Dohan, D., Gillpatrick, T., Robertson, K., & James, G. (1986). Leveraged decision making in advertising: the flat maximum principle and its implications, Journal of Marketing Research, 23 (1), 25-32.

Vasilash, G. (1996). The important numbers for manufacturing efficiency. Automotive Production, 108 (7), 18-19.

Valsic, W., Naughton, K., & Kerwin, K. (1998). If Ford can do it, why can't GM? Business Week, 36,(3584), 36-37.

Wamack, J., Jones, D., & Roos, D. (1990). The Machine that Changed the World, Rawson Associates, New York

Ward's Auto World (1999). What overcapacity? ..August, 30.

Zellner, A (1962). An efficient method of estimating seemingly unrelated regressions and tests of aggregation bias. Journal of the American Statistical Association, 57, 348-368.

Zhu, J., (2001) "Supper-efficiency and DEA sensitivity analysis." European Journal of Operational Research, 129 (2), 443-455.

Khaled Alshare, Emporia State University Xueming Luo, State University of New York, Fredonia Hani I. Mesak, Louisiana Tech University

Table 1
OLS RESULTS OF THE RELATIONSHIP BETWEEN EACH DEPENDENT VARIABLE
AND ALL INDEPENDENT VARIABLES

 Dependent Variable
 Y1 = Sales Volume

Independent Parameter Probability White's VIF
Variables Estimate >|T| Probability
 >|T|

Advertising 0.5231 0.0000 0.0000 1.32
Total assets 0.1943 0.0000 0.0000 1.06
Employees 0.6324 0.0000 0.0000 1.37

F-Statistics 274.50 ***
Adj. R-Square 0.96
Durbin - Watson 1.997

 Dependent Variable
 Y2 = Market Share

Independent Parameter Probability White's VIF
Variables Estimate >|T| Probability
 >|T|

Advertising 0.3605 0.0175 0.0135 1.32
Total assets 0.1107 0.1421 0.0932 1.06
Employees 0.5214 0.0000 0.0000 1.37

F-Statistics 79.65 ***
Adj. R-Square 0.89
Durbin - Watson 1.851

Note: all variables are expressed in terms of their natural logarithms.

*** p < .01

Table 2
STABILITY SCORES FOR THE SELECTED THREE 4-YEAR WINDOWS*

 Window 94-97

DMU CCR BCC
 stability stability

CR97 -0.0301 -0.0243
CR96 0.04769 0.06399
CR95 -0.0355 -0.0284
CR94 0.08326 0.25446
FD97 -0.0163 0.02323
FD96 0.03153 0.04775
FD95 0.01804 0.01863
FD94 0.00366 0.00996
GM97 -0.0228 0.07955
GM96 -0.0162 -0.0023
GM95 0.0075 0.0084
GM94 0.02225 0.02757

 Window 90-93

DMU CCR BCC
 stability stability

CR93 0.08251 0.09526
CR92 0.0306 0.06579
CR91 0.02259 0.05517
CR90 -0.004 0.01457
FD93 0.0365 0.06612
FD92 0.02253 0.02284
FD91 0.00553 0.00684
FD90 0.09778 0.09894
GM93 0.0034 0.04601
GM92 0.02269 0.04903
GM91 -0.0205 -0.0783
GM90 -0.0155 0.01795

 Window 86-89

DMU CCR BCC
 stability stability

CR89 0.08691 0.10147
CR88 0.00068 0.06849
CR87 -0.0166 -0.0018
CR86 0.32966 0.28617
FD89 0.00755 0.02418
FD88 0.01707 0.02836
FD87 -0.0279 0.00455
FD86 0.07669 0.09738
GM89 -0.1352 0.02362
GM88 0.0896 0.09513
GM87 -0.0466 0.19312
GM86 0.02739 0.08467

*. Numbers in bold mean efficient stable

Table 3
THE NUMBER OF EFFICIENT YEARS DURING EACH 4-YEAR WINDOW FOR CCR
AND (BCC) MODELS

Company # of # of # of Total
 efficient efficient efficient
 years years years
 1994-1997 1990-1993 1986-1989

Chrysler 2 (2) 3 (4) 3 (3) 8 (9)
Ford Motors 3 (4) 4 (4) 3 (4) 10 (12)
General Motor 2 (3) 2 (3) 2 (4) 6 (10)

Table 4
SPEARMAN'S CORRELATION COEFFICIENT OF STABILITY SCORES OF CCR VS. BCC

4-year windows Spearman Correlation Coefficient r (p-value)

1994-1997 0.671 (0.016)
1990-1993 0.930 (0.00001)
1986-1989 0.601 (0.0386)