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2004-01-2705 Evaluating Agricultural Tractor Performance: A Data Envelopment Analysis Approach Jeffrey R. Stokes Pennsylvania State University Paul W. Claar Strategic Technology Innovation Copyright © 2004 SAE International ABSTRACT Data envelopment analysis (DEA) is used to examine the efficiency of 74 front wheel assist agricultural tractors from three U.S. manufacturers. The outputs of drawbar horsepower and power takeoff horsepower are modeled in a constant returns-to-scale framework using three productive performance inputs (fuel consumption, slip, and center of gravity), and one price input, namely, retail tractor price. The results suggest that by and large, John Deere tractors are more DEA efficient than their competitor’s tractors. However, competitor’s tractors that are DEA efficient are most often the top benchmarks for DEA inefficient tractors. These results suggest that while John Deere appears to produce many quality tractors, competitor’s like CNH and AGCO produce a few tractors that may be of even higher quality. INTRODUCTION The U.S. market for agricultural tractors has evolved over the last century from a structure with numerous small manufacturers, each producing at most one brand to essentially three large manufacturers each producing at least two tractor brands. 1 For example, CNH manufactures Case-IH tractors as well as the New Holland line of tractors, and AGCO manufactures Allis, White, and Massey Ferguson brands of tractors. Among the large (i.e., over 100 horsepower) U.S. agricultural tractor manufacturers, only John Deere continues to produce a single tractor brand. Despite producing only one line of tractors, John Deere has a commanding presence in terms of market share in the U.S. and international agricultural equipment markets. One might wonder whether these tractors are really that much better than their competition, and if so, what factors contribute to their performance. 1 In 1909 there were 31 U.S. agricultural tractor manufacturing firms. Today, there are essentially three: AGCO, CNH, and John Deere. Performance measurement and its relationship to the measurement of the efficiency of agricultural tractors is not a new topic of research. Numerous studies have been conducted to measure efficiency from an engineering perspective. Product development engineers have developed parameters such as Tractive Efficiency (TE) and Power Delivery Efficiency (PDE) to evaluate and compare tractor performance [1-3]. PDE is defined as the ratio of a tractor’s delivered drawbar power to its vehicle input power while TE is the ratio of output power to input power of the tractive device. According to Zoz et al. [1-2], PDE gives a more complete and meaningful understanding of performance differences and includes TE and the efficiencies of the entire traction vehicle drivetrain from engine to drawbar. TE does not consider drivetrain and other efficiency losses; hence it is effectively a component of PDE. Engineering definitions of efficiency, such as PDE and TE, are by design, single input-single output measures. That is, they seek to measure the efficiency of a tractor in producing a single output by expressing it relative to a single input. Intuitively, multiple inputs and/or multiple outputs might provide more meaningful efficiency estimates and provide for more meaningful performance comparisons. However, a weighting scheme would be required for such a measurement and it is unclear how the weights for the various inputs and outputs should be determined. As demonstrated by Bulla, Cooper, and Wilson [4], Data Envelopment Analysis (DEA) can overcome this drawback by endogenizing the determination of the weights in a multi-input, multi-output setting using a linear programming approach. Compared to regression, such an approach also offers the advantage of being nonparametric in nature. In this study, the technical specifications and performance information for 74 agricultural tractors from three U.S. manufacturers are considered to determine which tractors are most efficient in delivering outputs using a predetermined set of inputs. Contrary too many previous applications of DEA where the Decision Making Unit (DMU) is a firm (e.g. a bank), the current study
Transcript

2004-01-2705

Evaluating Agricultural Tractor Performance: A Data Envelopment Analysis Approach

Jeffrey R. Stokes Pennsylvania State University

Paul W. Claar Strategic Technology Innovation

Copyright © 2004 SAE International

ABSTRACT

Data envelopment analysis (DEA) is used to examine the efficiency of 74 front wheel assist agricultural tractors from three U.S. manufacturers. The outputs of drawbar horsepower and power takeoff horsepower are modeled in a constant returns-to-scale framework using three productive performance inputs (fuel consumption, slip, and center of gravity), and one price input, namely, retail tractor price. The results suggest that by and large, John Deere tractors are more DEA efficient than their competitor’s tractors. However, competitor’s tractors that are DEA efficient are most often the top benchmarks for DEA inefficient tractors. These results suggest that while John Deere appears to produce many quality tractors, competitor’s like CNH and AGCO produce a few tractors that may be of even higher quality. INTRODUCTION

The U.S. market for agricultural tractors has evolved over the last century from a structure with numerous small manufacturers, each producing at most one brand to essentially three large manufacturers each producing at least two tractor brands.1 For example, CNH manufactures Case-IH tractors as well as the New Holland line of tractors, and AGCO manufactures Allis, White, and Massey Ferguson brands of tractors. Among the large (i.e., over 100 horsepower) U.S. agricultural tractor manufacturers, only John Deere continues to produce a single tractor brand. Despite producing only one line of tractors, John Deere has a commanding presence in terms of market share in the U.S. and international agricultural equipment markets. One might wonder whether these tractors are really that much better than their competition, and if so, what factors contribute to their performance.

1 In 1909 there were 31 U.S. agricultural tractor manufacturing firms. Today, there are essentially three: AGCO, CNH, and John Deere.

Performance measurement and its relationship to the measurement of the efficiency of agricultural tractors is not a new topic of research. Numerous studies have been conducted to measure efficiency from an engineering perspective. Product development engineers have developed parameters such as Tractive Efficiency (TE) and Power Delivery Efficiency (PDE) to evaluate and compare tractor performance [1-3]. PDE is defined as the ratio of a tractor’s delivered drawbar power to its vehicle input power while TE is the ratio of output power to input power of the tractive device. According to Zoz et al. [1-2], PDE gives a more complete and meaningful understanding of performance differences and includes TE and the efficiencies of the entire traction vehicle drivetrain from engine to drawbar. TE does not consider drivetrain and other efficiency losses; hence it is effectively a component of PDE.

Engineering definitions of efficiency, such as PDE and TE, are by design, single input-single output measures. That is, they seek to measure the efficiency of a tractor in producing a single output by expressing it relative to a single input. Intuitively, multiple inputs and/or multiple outputs might provide more meaningful efficiency estimates and provide for more meaningful performance comparisons. However, a weighting scheme would be required for such a measurement and it is unclear how the weights for the various inputs and outputs should be determined. As demonstrated by Bulla, Cooper, and Wilson [4], Data Envelopment Analysis (DEA) can overcome this drawback by endogenizing the determination of the weights in a multi-input, multi-output setting using a linear programming approach. Compared to regression, such an approach also offers the advantage of being nonparametric in nature.

In this study, the technical specifications and performance information for 74 agricultural tractors from three U.S. manufacturers are considered to determine which tractors are most efficient in delivering outputs using a predetermined set of inputs. Contrary too many previous applications of DEA where the Decision Making Unit (DMU) is a firm (e.g. a bank), the current study

DEA INPUTS AND OUTPUTS - To conduct the estimation in Equation (1), the vectors of inputs (x) and outputs (y) must be specified. Obvious outputs for an agricultural tractor include drawbar horsepower and power takeoff (PTO) horsepower. More clearly, a tractor is capable of producing two kinds of output related to its ability to pull an implement (drawbar horsepower) such as a plow, and operate other implements (PTO horsepower) such as forage equipment. All else equal, higher drawbar and PTO horsepower is more desirable.

treats each tractor as the relevant DMU. Hjalmarsson and Odeck [5] took a similar approach to investigate the efficiency of road construction trucks as did Bulla, Cooper, and Wilson [4] in examining the efficiency of turbo fan jet engines.

To determine the efficient set of tractors, the Charnes, Cooper, and Rhodes (CCR) constant returns-to-scale DEA methodology [6] is employed. The results of the DEA analysis are then further analyzed to help identify factors that contribute to and detract from a tractor’s relative performance and efficiency. In the sections that follow, the DEA model and data to be used are described in detail. Then, the results from the estimation of tractor efficiency scores and the determination of benchmarks are discussed. Lastly, concluding remarks are made.

On the input side, two types of inputs are modeled, namely, productive performance inputs and a price input. The most obvious choice for a productive performance input is fuel consumption as this is the most critical input for generating drawbar and PTO horsepower. Lower fuel consumption is a more desirable trait in a tractor. Other potential productive inputs would relate primarily to tractor design such as engine size (CID), number of cylinders, bore and stroke, tractor weight, etc. For our purposes, two inputs in addition to fuel consumption were chosen to measure efficiency, namely, slip and center of gravity.

DATA ENVELOPMENT ANALYSIS

DEA MODEL - As noted above, the DEA model implemented to examine tractor efficiency is the Charnes, Cooper, Rhodes (CCR) constant returns-to-scale methodology with an input orientation. The CCR approach is implemented as a dual linear program expressed for each DMU j as

Slip is the ratio of the difference between the theoretical and actual travel speed of a tractor to the theoretical speed, and is measured in percentage terms [3]. In this context, slip represents a loss in efficiently transferring power from the engine to the drive wheels of the tractor. Such a loss undermines the ability of the tractor to generate drawbar horsepower. Less slip is more desirable.2 iyy

mxx

jik

jkki

kjkkmjmjjk

j

∀≥λ

∀λ≥θλ

θmin

∑∑

The center-of-gravity (CG) of a tractor is the point at which the whole mass and weight may be considered to act, and is measured along its longitudinal wheelbase (i.e., length) that distributes its weight between the front and rear axles of the tractor [3]. Thus, the CG is longitudinally located at a point somewhere between the centerlines of the front and rear axles. The more weight that is distributed to the rear wheels of a tractor, the less slip the tractor typically generates, the more efficient is the delivery of drawbar horsepower. This implies that a lower value of the center-of-gravity (i.e., measured as a percentage of the distance from the CG to the centerline of the rear axle of the tractor to its wheelbase) is desirable.

where m and i index inputs (x) and outputs (y) and k indexes all DMUs (i.e. tractors) under investigation. The program seeks to find an optimal set of weights (denoted by λ) that satisfy the constraints in (1) and give rise to an efficiency score denoted by θ. Since we are dealing with a dual problem in (1), the optimal weights are the shadow prices associated with the primal problem. Also, the sum of the weights for each tractor j gives an estimate of the returns-to-scale with ∑ indicating

increasing returns-to-scale and indicating

decreasing returns-to-scale. The magnitude of the weights also gives information about relevant benchmarks for each inefficient tractor. This is an important point in that it is the model solution that determines the benchmarks for inefficient DMUs, not analysts or manufacturers.

0<λk

jk

∑k

jk 0>λ

Lastly, a non-productivity input is also modeled, i.e., the “f.o.b. price” of a tractor, which represents management’s input into the tractor. A given tractor’s price reflects the extent of its technology enhancements and includes research and development recovery as a component. Management prices tractors to be consistent with demand expectations, capital recovery, and corporate profitability targets. Lower tractor prices are more desirable in this context. Taking price into

Bulla, Cooper, and Wilson have analytically shown how the concept of optimality arising in a system such as Equation (1) can be reconciled with the concept of engineering efficiency. This result is important for the research in this study since the application of the concept of DEA efficiency should be internally consistent with that of engineering efficiency.

2 As pointed out by an anonymous reviewer, extremely low wheel slip creates higher peak loads on the drive train. Depending on the surface, optimum slip may be in the 7% to 16% range.

consideration is an important feature of the model since a tractor that is DEA efficient in its ability to use productive inputs to generate productive outputs might also do so at an inefficient price. In this case, the DEA model can be used to help determine the extent to which product pricing enhances or undermines DEA efficiency.

DATA - Nebraska Tractor Test reports provide useful technical specifications and performance results on most domestic tractors. Downs and Hansen [7-8] and Grisso and Pitman [9] describe the test procedures established by the Nebraska Tractor Test Laboratory. Each report provides the following information: (1) specific information about the tractor model and its specifications (such as, weight, center-of-gravity, ballast, etc.), (2) maximum and varying power and fuel consumption and efficiency (PTO performance), (3) varying drawbar power and fuel consumption (drawbar performance), (4) maximum power with and without ballast (drawbar performance), (5) varying drawbar pull and travel speed with ballast (drawbar performance), and (6) tractor sound level. From these test reports, all productive inputs can be measures. Tractor f.o.b. price data were obtained from the 2002 Official Guide [10]. The data used in the study for each of the 74 tractors are reported in Appendix Table 1.

EMPIRICAL RESULTS

The efficiency estimation was conducted using software developed by Zhu [11]. Input and output slacks are determined for each DMU, as well as, shadow prices which give information regarding the appropriate benchmarks for the identified inefficient tractors. In addition, returns-to-scale information provided.

TRACTOR DEA EFFICIENCY SCORES - Presented in Table 1 are the tractors ranked by DEA efficiency score along with the associated input and output slacks. As shown in Table 1, 18 tractors were identified as DEA efficient (i.e. radial efficiency score equal to 1) with the remaining 56 tractors identified as DEA inefficient (i.e. radial efficiency score less than 1). The 18 DEA efficient tractors form the DEA frontier below which all of the remaining tractors fall.

The information presented in Table 1 should be interpreted in the following manner. Using the Case-IH MX 80C as an example (ranked last), the efficiency score is θ* = 0.7747 which indicates that to become DEA efficient, this particular tractor would have to reduce its use of all inputs by 1 – θ* = 22.53% and then simultaneously decrease its slip by 0.96%, reduces its center of gravity by 9.44% (i.e., move towards the centerline of the rear drive axle), and reduce its price by $7,395. From this description, it is most likely the case that CNH has invested too much in the technology of the MX 80C relative to its performance, since the tractor is overpriced relative to its ability to deliver horsepower. Other inefficient tractors can be interpreted in a similar manner.

In looking at the table, several other results are apparent. First, fuel consumption efficiency is generally not a problem with modern agricultural tractors. Only four tractors could stand to improve their fuel consumption efficiency (beyond that suggested by their overall input inefficiency) and in each instance, the necessary improvement would need to be very small (about 0.4 to 1.9 HP hr/gal) to make these tractors efficient with respect to this input. Interestingly, three of the four tractors are Case-IH tractors and none are John Deere tractors.

The remaining productivity-oriented inputs (i.e., slip and center-of-gravity or CG) appear to go hand-in-hand in terms of inefficiency. This is not unexpected since the center of gravity of a tractor, and its attendant slip, are correlated. These inputs reflect the form and function of the tractor’s architecture (the geometric and inertial properties of the tractor’s powertrain components and operator’s station and cabin). In looking at the results, the most input inefficient tractors tend to be those that have a high CG value (measured as a percentage from the CG to the rear axle of the tractor) and generate significant slip. Price inefficiency is also most pervasive for highly inefficient tractors. These tractors are almost universally AGCO and CNH tractors.3

Output inefficiency is generally linked with respect to drawbar horsepower (i.e., the conversion of rotary motion of the powertrain to the linear motion of the drawbar of the tractor [3]). Only two tractors (both produced by AGCO) are inefficient in generating PTO horsepower (i.e., the conversion of the rotary motion of the powertrain to rotary motion of an output shaft to deliver power to attached implements [3]). The remaining output inefficiencies are related to drawbar horsepower and are all very marginal ranging from less than a half horsepower to about 14 horsepower. From these results, we can conclude that the DEA efficiency of agricultural tractors appears to be most influenced by inputs as opposed to outputs. Further, center-of-gravity and slip (i.e., function of the tractor architecture) appear to be the sources of most of the inefficiencies with price inefficiency generally playing a role in the most DEA inefficient tractors.

STATISTICAL TEST OF MEANS - A test of means was conducted to determine whether there was any statistical difference between the 18 DEA efficient and the 56 DEA inefficient tractors with respect to their outputs. The results presented in Table 2 suggest that the two groups are quite different. More specifically, the mean PTO horsepower for the DEA efficient (inefficient) tractors is 162 (104) and the means are statistically different at the 1% confidence level. Similarly, the mean drawbar horsepower for the DEA efficient (inefficient) tractors is 133 (84) and the means are statistically different at the 1% confidence level. From this, one can conclude that DEA efficient tractors tend to be larger 3 The least DEA efficient John Deere tractor is ranked 44th out of 74 tractors.

tractors (in terms of their drawbar and PTO horsepower outputs).

RETURNS TO SCALE AND BENCHMARKING - The question remains as to which brand of tractors are most DEA efficient and most often benchmarked. Presented in Table 3 are returns-to-scale and benchmark information for the 56 tractors identified as being DEA inefficient. In most cases, the returns-to-scale identified by the model are increasing. Furthermore, Figure 1 provides information regarding the incidence of benchmarks by tractor and manufacturer. For example, DMU 51, which is identified as the New Holland TS 110, is the most frequently referenced benchmark for inefficient tractors being referenced 16 times.

Interestingly, DMUs 30 (Case-IH MX220) and 67 (Massey-Ferguson 6270) are tied for second-place in terms of being the most frequently referenced benchmark. Despite John Deere’s relatively high incidence of DEA efficient tractors, they are less frequently a top benchmark for other inefficient tractors. While John Deere tractors tend to be DEA efficient and are often top benchmarks for inefficient tractors, each tractor manufacturer has at least one tractor in their line that is not only DEA efficient, but is also an overwhelming choice for a top benchmark. The New Holland TS 110 tractor, for example, is a top benchmark for 16 of the 54 DEA inefficient tractors and a top three benchmark for nearly one-third of all DEA inefficient tractors.

COMPARISON OF DEA EFFICIENT COMPETITORS - In the group of 19 DEA efficient tractors, four tractors (i.e., DMU 51, 67, 58, and 5) develop approximately 100 HP (pto) and directly compete with each other in the marketplace. Any one of the four tractors is a substitute for the other three tractors. Two tractors (New Holland TS 110 and Massey-Ferguson 6270) of the four are the top two frequently referenced benchmarks while the other two are not frequent benchmarks. Upon examining the Nebraska Tractor Test reports for these four tractors, one may observe the significance of tractor architecture on DEA efficiency, and other engineering and economic considerations. Summarized in Tables 4 are key performance and attribute information for these four tractors, several derived parametric values from this information to help compare and evaluate the tractors. Observe the following. Two different brand (i.e., New Holland and Deere) tractors have nearly the same weight and wheelbase, while the Massey tractors have longer wheelbases and greater weight difference. Likewise, the price difference between the New Holland and Deere tractors is smaller when compared to the Massey tractors. At first glance, the New Holland and Deere appear to be perfectly matched.

Next, several derived parametric values are used to compare and evaluate the four tractors. The first “rule-of-thumb” considers the price per unit of weight of the tractor (expressed in $ / lb). From Table 4, the parametric values are 3.91, 4.76, 3.86, and 3.89 ($/lb)

for the New Holland TS 110, Massey-Ferguson 6270, Massey-Ferguson 4260, and Deere 6410 models, respectively. Thus, it costs more to buy one pound of the Massey 4260 compared to the other three tractors. Next, the second and third “rule-of-thumb” considers the price to buy one PTO horsepower and one drawbar horsepower, respectively. From Table 4, the ($ / HP – pto) parametric values for the New Holland and Deere tractors are more similar than are the Massey tractors. The ($ / HP – db) parametric values for the four tractors are more variable. The Deere value is the highest since this tractor was not as efficient developing drawbar horsepower compared to the other three tractors. For all three “rules-of-thumb,” the smaller the parametric values, the better it is.

Next, Zoz’s Power Delivery Efficiency (PDE) is computed. The Massey 6270 performs best (i.e., 95.09%) while the Deere 6410 performs worse (i.e., 76.33%). The PDE for the New Holland and Massey 4260 are 84.04% and 82.40%. The average PDE of the 19 DEA efficient tractors is 83.38% while the average PDE of the DEA inefficient tractors is 81.6%. Thus, the PDE for the New Holland and Massey 4260 are essentially average for the group of tractors. Thus, there is no correlation between DEA efficiency and PDE measure.

Another parametric value is the ratio of the vehicle weight carried by the tractor’s rear axle to drawbar horsepower developed by the specific tractor. A lower valued ratio would indicate that a tractor’s output is more efficient given the inputs. The values of this ratio indicate that the Massey tractors are more efficient in the sense that less rear axle weight is needed for each unit of drawbar horsepower. The fifth and last “rule-of-thumb” is that static distribution of tractor weight on the axles. In Table 4, the percent of the total tractor weight carried by the rear axle is presented. Traditionally, tractor manufacturers have suggested that the 60% of the tractor weight should be carried on the rear drive axle. The results indicate the four tractors carried approximately 60% of the vehicle weight on the rear axle. From a DEA efficiency perspective, the New Holland tractor is the best in this group.

The results indicate that for at least the 74 tractors analyzed, vehicle architecture (i.e., center-of-gravity and slip) contributes more to their DEA efficiency than powertrain efficiency (i.e., fuel consumption performance) does. The four “100 HP” tractors are used to verify these results. Two tractors have shorter wheelbases (i.e., the New Holland and Deere) compared to the two Massey tractors. The shorter wheelbase allows the New Holland and Deere tractors to be more maneuverable (e.g., shorter turning radius). Also three of the four tractors (i.e., New Holland, Deere and Massey 6270) have essentially the same amount of gross vehicle weight on the rear drive axle. Thus these three tractors have essentially equivalent tractive performance efficiency characteristics. To verify this claim, Zoz’s “Tractive Performance” spreadsheet (described in

Reference [2]) was used. The simulated tractive performance results for these three tractors were essentially identical. The results for the Massey 4270 were comparable. Again, the vehicle weight and wheelbase attributes affect other tractor performance characteristics. A ‘lighter’ vehicle (i.e., less weight) influences other engineering considerations (such as ride and handling), manufacturing (such as less material and handling costs) and profitability.

CONCLUSION

It is often said that the green paint on John Deere tractors adds price/value. An analysis of tractor data from various U.S. manufacturers reveals that John Deere tractors are generally more DEA efficient that their competitor’s tractors in using productive and price inputs to generate horsepower output. This result seems to suggest that while John Deere tractors may have brand appeal, on average, they are of high enough quality to justify a higher price. However, this is not to say that AGCO and CNH tractors are inferior across the board. In fact, a Massey Ferguson tractor (made by AGCO) and two CNH tractors (a New Holland and Case-IH tractor) are top benchmarks for the majority of DEA inefficient tractors. Despite the generally high quality of John Deere’s product as measured by DEA efficiency, competitor tractors are often times the industry standard.

Preliminary results suggest that the DEA methodology could be used as a product planning tool, particularly when interfaced to computer-aided engineering methodologies. For agricultural tractor development, DEA could serve as a guide to optimize future prototype tractor model development, particularly in terms of tractor architecture to evaluate form and function considerations.

REFERENCES

1. Zoz, F.M., R.J. Turner, and L.R. Shell. 2002. “Power Delievery Efficiency: A Valid Measure of Belt and Tire Tractor Performance.” Transactions of the ASAE 45(3):509-518.

2. Zoz, F.M and R.D. Grisso. 2003. “Traction and Tractor Performance,” ASAE Distinguished Lecture Series - Tractor Design No. 27. St. Joseph, MI.

3. Macmillan, R.H. 2002. The Mechanics of Tractor-Implement Performance: Theory and Worked Examples. University of Melbourne, available at http://eprints.unimelb.edu.au/archive/00000204.

4. Bulla, S., W.W. Cooper, and D. Wilson. 2000. “Evaluating Efficiencies of Turbofan Jet Engines: A Data Envelopment Analysis Approach,” Journal of Propulsion and Power 16(3): 431-439.

5. Hjalmarsson, L. and J. Odeck. 1996. Efficiency of trucks in road construction and maintenance: An evaluation with data envelopment analysis. Computers Ops. Res. 23:393-404.

6. Cooper, W.W., L.M. Seiford, and K.Tone. 2000. Data envelopment analysis: a comprehensive text

with models, applications, references, and DEA-Solver software. Kluwer Academic Pub., Boston.

7. Downs, H.D. and R.W. Hansen. (1996a). “Estimating Farm Fuel Requirements,” Farm and Ranch Equipment Series No. 5.006. Colorado State University Cooperative Extension, Ft. Collins, CO.

8. Downs, H.D. and R.W. Hansen. (1996b). “Selecting Energy-Efficient Tractors,” Farm & Ranch Equipment Series No. 5.007. Colorado State University Cooperative Extension, Ft. Collins, CO.

9. Grisso, R. and R. Pitman. (2001). “Gear Up and Throttle Down,” Publication 442-450. Virginia Cooperative Extension, Blacksburg, VA.

10. _____ 2002 Official Guide, Iron Solutions LLC, Fenton, MO 63026-3480.

11. Zhu J., 2002 Quantitative Models for Performance Evaluation and Benchmarking: DEA with Spreadsheets and DEA Excel Solver Kluwer Academic Publishers, Boston, MA. DEA Frontier, Excel Add-in software also available at http://www.deafrontier.com.

CONTACT

Jeffrey R. Stokes is Associate Professor, Department of Agricultural Economics and Rural Sociology, Pennsylvania State University, University Park, PA 16802, email: [email protected].

Table 1. DEA Efficient and Inefficient FWD Tractors, Efficiency Scores, and Input and Output Slacks. Input Slacks Output Slacks

Rank Make Model DMU Radial Efficiency

Fuel Consumption (HP

hr/gal)

Slip (%)

Center of Gravity (% rear)

Price ($) PTO HP Drawbar

HP

1 John Deere 6410 5 1.0000 - - - - - -2 John Deere 7810 IVT 9 1.0000 - - - - - - 3 John Deere 8210 11 1.0000 - - - - - -4 John Deere 8410 13 1.0000 - - - - - -5 John Deere 8520 14 1.0000 - - - - - -6 White 6810 16 1.0000 - - - - - -7 White 8710 20 1.0000 - - - - - -8 White 8810 21 1.0000 - - - - - -9 Case-IH C 90, CX 90 26 1.0000 - - - - - -

10 Case-IH C 100, CX 100 27 1.0000 - - - - - - 11 Case-IH MX 200 29 1.0000 - - - - - -12 Case-IH MX 220 30 1.0000 - - - - - -13 New Holland TS 110 51 1.0000 - - - - - - 14 Massey Ferguson 4260, 4263, 4360 62 1.0000 - - - - - - 15 Massey Ferguson 6270 67 1.0000 - - - - - -16 Massey Ferguson 6280 68 1.0000 - - - - - -17 Massey Ferguson 8240 71 1.0000 - - - - - -18 Massey Ferguson 8250 72 1.0000 - - - - - -19 AGCO Allis 5660 53 0.9979 - 13.1332 24.9522 - - -20 John Deere 6310 SyncroPlus 4 0.9914 - - 4.9468 - - 1.941 21 John Deere 8310 12 0.9903 - 2.0589 - $ 5,484 - 4.798 22 Massey Ferguson 8220 70 0.9892 - 1.1676 - - 16.138 - 23 Case-IH C 80, CX 80 25 0.9888 0.4348 - 4.6477 - - 2.42824 John Deere 8110 10 0.9884 - - 0.0613 - - - 25 New Holland TL 90 37 0.9880 - - 11.1506 - - 6.229 26 AGCO Allis 5650 52 0.9876 - 11.3778 27.2235 - - - 27 Case-IH MX 240 31 0.9826 - - - $ 9,291 - 1.427 28 John Deere 7710 8 0.9800 - 0.2930 - - - - 29 John Deere 6310 3 0.9799 - - 4.3445 - - 1.44130 Case-IH MX 270 32 0.9795 1.8848 - - - - 0.42531 New Holland TS 100 49 0.9795 - - 5.5690 - - 1.665 32 Massey Ferguson 4233, 4335 60 0.9767 - 0.8354 8.4218 - - - 33 Case-IH C 60, CX 60 23 0.9708 - - 17.4922 - - - 34 Massey Ferguson 6290 69 0.9669 - 2.9511 - - - -35 John Deere 6210 2 0.9655 - - 6.6311 - - 2.79236 Whitea 8410 17 0.9651 - 0.4625 - - - -37 John Deere 7610 7 0.9639 - 0.1100 - $ 489 - - 38 John Deere 7510 6 0.9535 - 0.9804 0.8833 $11,728 - -

39 New Holland TS 90 50 0.9513 - - 11.2363 - - - 40 Massey Ferguson 4255, 4253 58 0.9473 - - 4.8770 - - 5.350 41 Massey Ferguson 4270, 4370 63 0.9440 - - 0.4102 - - 3.121 42 New Holland TM 165 43 0.9437 0.5531 1.7187 - - - - 43 Case-IH 180 28 0.9394 - 0.0000 0.3994 - - 13.89644 John Deere 6110 1 0.9383 - 0.0047 10.8459 - - - 45 New Holland TL 100 38 0.9346 - 0.6055 9.0284 - - - 46 Whiteb 8610 19 0.9308 - 0.2984 - - - -47 New Holland TL 80 36 0.9308 - 0.0000 14.1501 - - 1.068 48 Massey Ferguson 4245, 4233 57 0.9268 - 0.0000 5.8797 - - 3.176 49 Massey Ferguson 8170, 8270 73 0.9267 - 0.0000 - - - 4.357 50 White 6045 15 0.9243 - 2.1806 25.6256 - - - 51 Massey Ferguson 243 54 0.9234 - 2.5999 18.8758 - - -

52 New Holland TN 70, 70D, TN 70S 46 0.9201 2.6799 18.7446 $ 2,230.06 - -

53 Massey Ferguson 8280 74 0.9139 1.0260 0.1954 - - - -54 Massey Ferguson 4245, 4243, 4345 61 0.9114 - - 6.1140 - - 2.090 55 Case-IH C 70, CX 70 24 0.9103 - - 8.6251 - - 0.844 56 Whitec 8510 18 0.9043 - - - - 14.829 -57 New Holland TL 70 35 0.9016 - - 17.3076 - - 1.880 58 New Holland TM 150 42 0.8960 - 0.4550 3.9050 - - - 59

New Holland TN 75D, TN 75S 47 0.8946 -

3.4624

13.9887$

1,346.02 - -

60 Massey Ferguson 6265 66 0.8904

- 3.0375

2.7643

$ 3,413.23

- -

61 New Holland TM 135 41 0.8871 - 0.0307 - - - - 62 New Holland TN 65 48 0.8824 - 0.5069 13.1122 - - - 63

Massey Ferguson 6245 64 0.8690 -

2.7275

13.1297$13,426.6

8 - -

64 New Holland TM 125 40 0.8684 - 1.4679 10.7057 - - - 65 Massey Ferguson 4225, 4325 59 0.8556 - - 13.2859 - - 1.583 66 Massey Ferguson 4235 56 0.8553 - 0.1867 14.8948 - - - 67 Case-IH C 50, CX 50 22 0.8541 - 0.5794 20.9502 - - - 68 New Holland TM 115 39 0.8540 - 1.4090 14.9155 - - - 69 Massey Ferguson 263 55 0.8417 - 2.8156 13.3932 - - -70

Massey Ferguson 6255 65 0.8350 -

2.2836

7.7863$

3,012.62 - -

71 New Holland TN 55D, TN 55S 44 0.8293

- 2.8692

19.3222

$ 4,273.39

- -

72 New Holland TN 65D, TN 65S 45 0.8279 - 2.7358 17.8807 - - - 73

Case-IH

MX 90C 34 0.7831-

0.2450 11.0955$

6,109.48 - -

74 Case-IH

MX 80C 33 0.7747

- 0.9593 9.4432

$ 7,394.95

- -

a The White 8410 is also the AGCO RT 145

b The White 8610 is also the AGCO DT 180 b The White 8510 is also the AGCO DT 160 and the AGCO Allis 9755.

Table 2. Test of Means between DEA Efficient and DEA Inefficient Tractors. Difference in Mean PTO Horsepower between DEA Efficient and DEA Inefficient Tractors Difference in Mean Drawbar Horsepower between

DEA Efficient and DEA Inefficient Tractors t-Test: Two-Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances Efficient Inefficient Efficient InefficientMean PTO HP 162.1911 103.9636 Mean Drawbar HP 132.6939 84.00411Variance 4520.01 3317.373 Variance 2440.825 1945.043Observations 18 56 Observations 18 56Hypothesized Mean Difference 0 Hypothesized Mean Difference 0 df 26 df 26 t Stat 3.305234 t Stat 3.730669 P(T<=t) one-tail 0.001386 P(T<=t) one-tail 0.00047 t Critical one-tail 1.705616 t Critical one-tail 1.705616 P(T<=t) two-tail 0.002772 P(T<=t) two-tail 0.00094 t Critical two-tail 2.055531 t Critical two-tail 2.055531

Table 4. Comparison of Tractor Attribute and Performance Data and Derived Parametric Values.

Tractor NH TS110 MF 6270 MF 4260 JD 6410

OCED Test # 1834 1860 1731 1806 DMU 51 67 58 5

Weight (lb) 9960 10305 9245 9845 Rear Wt. (lb) 6170 6140 5465 6160 Wheelbase (in) 93 106.3 102.7 94.5 HP - pto 98.4 103.9 94.9 98 HP - db 82.7 98.8 78.2 74.8 Price ($) 38987 49020 35695 38278

Parametric Value $ / lb 3.91 4.76 3.86 3.89 $ / HP - pto 396.21 471.80 376.13 390.59 $ / HP - db 471.43 496.15 456.46 511.74 PDE 84.04% 95.09% 82.40% 76.33% Rear Wt / HP - db 74.61 62.15 69.88 82.35 % weight - rear 61.95% 59.58% 59.11% 62.57%

Table 3. DEA Inefficient FWD Tractors, Returns to Scale, and Top Three Benchmarks. Returns to Scale Benchmarks Rank Make Model DMU

DMU Benchmark #1 DMU Benchmark #2 DMU Benchmark #3 19 AGCO Allis 5660 53 increasing 67 Massey Ferguson 6270 51 New Holland TS 110 11 John Deere 8210 20 John Deere 6310 4 increasing 5 John Deere 6410 51 New Holland TS 110 29 Case-IH MX 200 21 John Deere 8310 12 decreasing 30 Case-IH MX 220 13 John Deere 8410 - - 22 Massey Ferguson 8220 70 increasing 71 Massey Ferguson 8240 9 John Deere 7810 IVT 68 Massey Ferguson 6280 23 Case-IH C 80, CX 80 25 increasing 26 Case-IH C 90, CX 90 9 John Deere 7810 IVT - - 24 John Deere 8110 10 decreasing 30 Case-IH MX 220 29 Case-IH MX 200 51 New Holland TS 110 25 New Holland TL 90 37 increasing 51 New Holland TS 110 5 John Deere 6410 29 Case-IH MX 200 26 AGCO Allis 5650 52 increasing 67 Massey Ferguson 6270 51 New Holland TS 110 11 John Deere 8210 27 Case-IH MX 240 31 decreasing 30 Case-IH MX 220 13 John Deere 8410 14 John Deere 8510 28 John Deere 7710 8 increasing 30 Case-IH MX 220 68 Massey Ferguson 6280 11 John Deere 8210 29 John Deere 6310 3 increasing 5 John Deere 6410 51 New Holland TS 110 29 Case-IH MX 200 30 Case-IH MX 270 32 increasing 14 John Deere 8510 13 John Deere 8410 11 John Deere 8210 31 New Holland TS 100 49 increasing 51 New Holland TS 110 5 John Deere 6410 29 Case-IH MX 200 32 Massey Ferguson 4233, 4335 60 increasing 30 Case-IH MX 220 11 John Deere 8210 67 Massey Ferguson 6270 33 Case-IH C 60, CX 60 23 increasing 51 New Holland TS 110 26 Case-IH C 90, CX 90 67 Massey Ferguson 6270 34 Massey Ferguson 6290 69 increasing 68 Massey Ferguson 6280 51 New Holland TS 110 11 John Deere 8210 35 John Deere 6210 2 increasing 51 New Holland TS 110 5 John Deere 6410 29 Case-IH MX 200 36 Whitea 8410 17 increasing 30 Case-IH MX 220 11 John Deere 8210 68 Massey Ferguson 6280 37 John Deere 7610 7 increasing 67 Massey Ferguson 6270 30 Case-IH MX 220 72 Massey Ferguson 8250 38 John Deere 7510 6 increasing 67 Massey Ferguson 6270 30 Case-IH MX 220 - - 39 New Holland TS 90 50 increasing 51 New Holland TS 110 67 Massey Ferguson 6270 30 Case-IH MX 220 40 Massey Ferguson 4255, 4253 58 increasing 51 New Holland TS 110 5 John Deere 6410 62 Massey Ferguson 4260d 41 Massey Ferguson 4270, 4370 63 decreasing 51 New Holland TS 110 5 John Deere 6410 29 Case-IH MX 200 42 New Holland TM 165 43 increasing 9 John Deere 7810 IVT 51 New Holland TS 110 68 Massey Ferguson 6280 43 Case-IH 180 28 increasing 9 John Deere 7810 IVT 29 Case-IH MX 200 16 White 6810 44 John Deere 6110 1 increasing 51 New Holland TS 110 11 John Deere 8210 5 John Deere 6410 45 New Holland TL 100 38 increasing 51 New Holland TS 110 5 John Deere 6410 11 John Deere 8210 46 Whiteb 8610 19 increasing 14 John Deere 8510 71 Massey Ferguson 8240 9 John Deere 7810 IVT 47 New Holland TL 80 36 increasing 51 New Holland TS 110 29 Case-IH MX 200 16 White 6810 48 Massey Ferguson 4245, 4233 57 increasing 51 New Holland TS 110 62 Massey Ferguson 4260d 26 Case-IH C 90, CX 90 49 Massey Ferguson 8170, 8270 73 decreasing 30 Case-IH MX 220 20 White 8710 9 John Deere 7810 IVT 50 White 6045 15 increasing 51 New Holland TS 110 67 Massey Ferguson 6270 11 John Deere 8210 51 Massey Ferguson 243 54 increasing 5 John Deere 6410 New Holland TS 110 62 Massey Ferguson 4260d 52 New Holland TN70, 70D, TN70S 46 increasing 67 Massey Ferguson 6270 30 Case-IH MX 220 - - 53 Massey Ferguson 8280 74 increasing 14 John Deere 8510 11 John Deere 8210 John Deere 8410 54 Massey Ferguson 4245, 4243, 4345 61 increasing 51 New Holland TS 110 62 Massey Ferguson 4260d 5 John Deere 6410 55 Case-IH C 70, CX 70 24 increasing 26 Case-IH C90, CX 90 51 New Holland TS 110 62 Massey Ferguson 4260d 56 Whitec 8510 18 increasing 30 Case-IH MX 220 9 John Deere 7810 IVT 14 John Deere 8510 57 New Holland TL 70 35 increasing 51 New Holland TS 110 29 Case-IH MX 200 5 John Deere 6410

58 New Holland TM 150 42 increasing 11 John Deere 8210 67 Massey Ferguson 6270 30 Case-IH MX 220 59 New Holland TN 75D, TN 75S 47 increasing 67 Massey Ferguson 6270 30 Case-IH MX 220 - - 60 Massey Ferguson 6265 66 increasing 67 Massey Ferguson 6270 30 Case-IH MX 220 - - 61 New Holland TM 135 41 increasing 11 John Deere 8210 67 Massey Ferguson 6270 51 New Holland TS 110 62 New Holland TN 65 48 increasing 51 New Holland TS 110 62 Massey Ferguson 4260d 5 John Deere 6410 63 Massey Ferguson 6245 64 increasing 67 Massey Ferguson 6270 30 Case-IH MX 220 - - 64 New Holland TM 125 40 increasing 11 John Deere 8210 67 Massey Ferguson 6270 51 New Holland TS 110 65 Massey Ferguson 4225, 4325 59 increasing 5 John Deere 6410 51 New Holland TS 110 29 Case-IH MX 200 66 Massey Ferguson 4235 56 increasing 5 John Deere 6410 11 John Deere 8210 51 New Holland TS 110 67 Case-IH C 50, CX 50 22 increasing 51 New Holland TS 110 11 John Deere 8210 67 Massey Ferguson 6270 68 New Holland TM 115 39 increasing 30 Case-IH MX 220 11 John Deere 8210 67 Massey Ferguson 6270 69 Massey Ferguson 263 55 Increasing 5 John Deere 6410 51 New Holland TS 110 11 John Deere 8210 70 Massey Ferguson 6255 65 Increasing 67 Massey Ferguson 6270 30 Case-IH MX 220 - - 71 New Holland TN 55D, TN 55S 44 increasing 30 Case-IH MX 220 67 Massey Ferguson 6270 - - 72 New Holland TN 65D, TN 65S 45 increasing 30 Case-IH MX 220 67 Massey Ferguson 6270 11 John Deere 8210 73 Case-IH MX 90C 34 increasing 67 Massey Ferguson 6270 30 Case-IH MX 220 - - 74 Case-IH MX 80C 33 increasing 67 Massey Ferguson 6270 30 Case-IH MX 220 - -

a The White 8410 is also the AGCO RT 145 b The White 8610 is also the AGCO DT 180 b The White 8510 is also the AGCO DT 160 and the AGCO Allis 9755 d Includes the Massey Ferguson 4263 and 4360

Figure 1. Incidence of Benchmarks by DMU and Manufacturer.

Frequency of Top Benchmark by Tractor

02468

1012141618

5 9 11 14 26 30 51 67 68 71

DM U

Freq

uenc

y

Frequency of A ll Benchmarks by Tractor

0

5

10

15

20

25

30

35

5 9 11 13 14 16 20 26 29 30 51 62 67 68 71 72

DM U

Freq

uenc

y

Frequency of Top Benchmark by Manufacturer

02

46

810

1214

1618

John Deere Case-IH New Holland Massey Ferguson

Manufacturer

Freq

uenc

y

Frequency of A ll Benchmarks by Manufacturer

0

10

20

30

40

50

60

John Deere White Case-IH New Holland MasseyFerguson

M anufacturer

Freq

uenc

y

Appendix Table 1. FWD Tractor Input and Output Data.

DMU Make and Model Fuel Consumptiona Slipb CGc Priced PTO HP Drawbar HP

1 John Deere 6110 8.54 3.20 37.58 $31,238 71.10 58.50 2 John Deere 6210 9.29 4.10 37.32 $32,632 78.60 61.80 3 John Deere 6310 9.93 7.10 37.78 $35,271 87.40 65.80 4 John Deere 6310e 9.82 6.20 37.22 $35,271 87.30 66.10 5 John Deere 6410 10.92 8.50 37.43 $38,278 98.00 74.80 6 John Deere 7510 13.36 3.61 35.12 $72,899 118.81 101.26 7 John Deere 7610 14.15 3.26 33.91 $67,320 126.83 108.47 8 John Deere 7710 16.38 3.66 34.60 $75,021 150.94 123.87 9 John Deere 7810 IVT 18.99 2.33 35.23 $79,422 167.58 139.47 10 John Deere 8110 19.63 3.81 40.83 $90,710 188.26 144.65 11 John Deere 8210 22.13 5.22 40.79 $100,926 214.65 165.18 12 John Deere 8310 24.08 6.26 40.56 $125,095 236.74 176.22 13 John Deere 8410 27.30 6.52 40.14 $135,877 269.98 203.49 14 John Deere 8510 31.06 4.36 40.71 $150,933 292.88 225.13 15 White 6045 5.51 4.00 43.66 $22,015 45.70 39.00 16 White 6810 13.90 3.86 36.20 $50,470 119.87 95.93 17 White 8410, AGCO RT 145 17.17 4.10 36.00 $78,365 155.91 127.52

18

White 8510, AGCO DT 160 AGCO Allis 9755 Diesel

(Cummins) 20.88 2.87 36.10 $100,865 168.30 142.58 19 White 8610, AGCO DT 180 23.29 4.34 35.83 $109,410 200.01 160.22 20 White 8710 26.48 2.79 37.31 $119,530 225.28 177.14 21 White 8810 28.63 3.12 37.25 $133,685 233.39 200.61 22 Case-IH C50, CX50 5.55 2.50 40.66 $21,402 42.50 35.40 23 Case-IH C60, CX60 6.81 2.40 40.86 $23,746 56.50 48.40 24 Case-IH C70, CX70 7.93 3.00 39.20 $25,349 59.70 50.20 25 Case-IH C80, CX80 9.41 3.10 39.94 $27,798 71.30 59.30 26 Case-IH C90, CX90 9.98 3.60 40.61 $30,197 79.70 69.20 27 Case-IH C100, CX100 11.31 5.00 40.68 $32,428 86.20 74.00 28 Case-IH MX180 20.17 2.67 38.40 $89,592 175.68 124.86 29 Case-IH MX200 19.49 2.80 37.25 $93,935 193.16 142.33 30 Case-IH MX220 21.04 2.92 37.84 $104,298 209.25 161.21 31 Case-IH MX240 24.30 4.06 39.58 $129,686 235.15 178.57 32 Case-IH MX270 30.98 4.65 39.05 $141,808 270.93 207.01 33 Case-IH MX80C 9.33 3.00 35.49 $52,201 67.80 57.30 34 Case-IH MX90C 10.23 2.20 39.09 $54,887 75.50 63.30 35 New Holland TL70 7.27 2.40 40.73 $27,618 58.90 45.80 36 New Holland TL80 8.26 2.90 40.73 $30,242 68.10 54.80 37 New Holland TL90 9.39 3.70 41.47 $33,442 81.50 61.00 38 New Holland TL100 10.01 5.00 40.68 $36,378 83.10 67.60 39 New Holland TM115 11.73 3.80 39.62 $55,768 98.00 76.20 40 New Holland TM125 13.29 4.90 39.77 $59,489 110.20 87.20 41 New Holland TM135 14.49 3.90 35.60 $61,629 118.70 98.20 42 New Holland TM150 15.33 4.00 37.12 $69,222 130.90 105.00 43 New Holland TM165 18.56 4.60 36.08 $73,707 148.30 125.00 44 New Holland TN55D, TN55S 5.43 4.40 35.67 $30,612 43.00 35.30 45 New Holland TN 65D, TN65S 6.61 4.40 35.92 $31,416 52.80 42.70

46 New Holland TN70, 70D,

TN70S 7.04 4.30 38.77 $34,131 60.10 51.60

47 New Holland TN75D, TN75S 7.71 5.40 35.92 $36,154 63.90 55.00 48 New Holland TN65 6.96 3.90 38.63 $23,288 52.70 43.50 49 New Holland TS100 10.22 5.20 39.70 $35,707 88.00 69.80 50 New Holland TS90 9.14 2.90 39.90 $35,146 77.20 65.70 51 New Holland TS110 11.38 4.50 38.05 $38,987 98.40 82.70 52 AGCO Allis 5650 5.47 13.00 45.85 $21,910 46.90 43.80 53 AGCO Allis 5660 6.33 15.00 42.84 $25,625 57.00 48.40 54 Massey Ferguson 243 5.83 6.50 40.23 $20,240 47.60 37.70 55 Massey Ferguson 263 7.12 7.40 39.53 $25,000 53.00 42.40 56 Massey Ferguson 4235 8.45 4.60 40.30 $33,600 67.10 51.60 57 Massey Ferguson 4245, 4233 9.87 4.10 40.29 $32,865 77.90 62.20 58 Massey Ferguson 4255, 4253 10.51 5.30 40.66 $36,013 86.70 65.60 59 Massey Ferguson 4225, 4325 7.37 4.60 39.32 $26,895 56.90 42.50 60 Massey Ferguson 4233, 4335 8.60 4.00 40.70 $28,085 69.70 60.20

61 Massey Ferguson 4245, 4243,

4345 9.95 4.10 40.29 $33,625 77.90 63.20

62 Massey Ferguson 4260, 4263,

4360 11.50 5.80 40.89 $35,695 94.90 78.30 63 Massey Ferguson 4270, 4370 12.21 6.30 40.92 $42,820 101.50 79.00 64 Massey Ferguson 6245 9.88 5.00 39.73 $60,605 80.50 68.00 65 Massey Ferguson 6255 11.10 5.00 39.41 $53,025 85.30 74.20 66 Massey Ferguson 6265 11.87 6.00 37.60 $55,400 95.60 85.40 67 Massey Ferguson 6270 11.98 3.00 40.22 $49,020 103.90 98.80 68 Massey Ferguson 6280 14.43 5.00 39.15 $53,570 111.30 114.30 69 Massey Ferguson 6290 15.19 8.00 39.95 $58,100 120.50 113.60 70 Massey Ferguson 8220 17.70 5.00 35.21 $76,235 135.40 133.60 71 Massey Ferguson 8240 18.02 5.00 36.47 $80,500 155.20 141.10 72 Massey Ferguson 8250 18.10 6.00 33.98 $97,030 165.80 144.80 73 Massey Ferguson 8170, 8270 25.59 3.10 40.83 $119,730 216.70 165.10 74 Massey Ferguson 8280 28.31 5.50 40.73 $130,895 239.40 183.00

Source: 2002 Nebraska Tractor Test Reports and 2002 Farm Equipment Official Guide a horsepower hours per gallon b unitless c percent from rear d last price f.o.b. factory (2001) e SynchoPlus


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