technical efficiency estimates for sarawak pepper farming...

Pertanika J. Soc. Sci. & Hum. 7(2): 103 - 110 (1999) ISSN: 0128-7702© Universiti Putra Malaysia Press

Technical Efficiency Estimates for Sarawak Pepper Farming:A Comparative Analysis

ALIAS RADAM and MOHD. MANSOR ISMAILJabatan Perniagaantani dan Sistem Maklumat,

Fakulti Ekonomi & Pengurusan,Universiti Putra Malaysia, 43400 UPM, Serdang,

Selangor, Malaysia

Keywords: technical efficiency, Sarawak pepper farming, comparative analysis

ABSTRAK

Menganggar kecekapan teknikal teknologi pengeluaran adalah penting untuk tujian polisi.Empat fungsi sempadan (frontier) pengeluaran terdiri dari fungsi berparameter dan tidakberparameter dianalisis untuk menganggar kadar kecekapan teknikal ke atas sampelladang ladahitam di Sarawak. Metadologi yang digunakan memberi anggaran taburan dan 'ranking' kadarkecekapan yang berbeza. Anggaran fungsi tidak berparameter adalah lebih tinggi berbandinganggaran fungsi berparameter kecuali di bawah kaedah stokastik berparameter. Disebabkan olehperbezaan yang ketara didalam keputusan kecekapan teknikal, cadangan untuk tujuan polisitidak boleh dibuat tanpa terlebih dahulu dibuat analisis terperinci bagi setiap kaedah yangdigunakan.

ABSTRACT

Estimating technical efficiency of production technology is important for policy purposes. Fourproduction frontiers consisting of parametric and nonparametric functions were analysed toestimate technical efficiency ratios on a sample of pepper farms in Sarawak. The methodologiesemployed produced different estimates, distributions, and rankings of efficiency ratios. Thenonparametric estimates were greater than parametric estimates except under stochastic parametricmethod. Due to the large ditferences in technical efficiency results, recommendation for policypurpose should not be made without prior detailed analysis of each method.

INTRODUCTION

The modeling of production activities has longoccupied a central role in applied economicresearch, both as an area in which existingstatistical estimators may be applied and inproviding a stimulus for the development of newmethods. In standard microeconomic theory,production technology is represented bytransformation (production) function thatdefines the maximum attainable outputs fromdifferent combinations of inputs. Hence, thetransformation function describes a boundaryor a frontier. Given that the production functionto be estimated had constant returns to scale,Farrell (1957) assumed that observed input perunit of output values for firms would be abovethe so-called unit isoquant. The unit isoquantdefmes the input per unit output ratios associated

with the most efficient use of inputs to producethe output involved. The deviation of observedinput per unit output ratios from the unitisoquant is considered to be associated withtechnical efficiency. On the other hand,technical inefficiency is defined as a firm's failureto produce maximum output from a given set ofinputs (Forsund et al., 1980).

A more general presentation of Farrells'concept of production (or frontier) is depictedin Fig. 1 involving the original input and outputvalues. The observed input-output values arebelow the production frontier, given that firmsdo not attain the maximum output possible forthe inputs involved, for a given technology. Ameasure of technical efficiency of the firm whichproduce output, y, with input, x, denoted bypoint A, is given by y/y*, where y* is frontier

Alias Radam and Mohd. Mansor Ismail

Output

Production Frontier

'\y B(X,Y*)

j *1*

!*

*

* • ~.' t".~.

Dbserved inputj Input values

xInput

Fig. 1. Technical efficiency offirms in input-output space

output associated with the level of input, x,(point B). Thus, the ratio of observed outputand frontier output is a measure of technicalefficiency for the input involved.

In recent years, many empirical studies usingfrontier function methodologies have beenundertaken with the purpose of measuring farmefficiency. Recent differences in farm efficiencymeasurements may have been the result ofnumerous factors, including the time periodanalysed, the degree of sample homogeneity,output aggregation and the method employed(Neff et at., 1991). For example, Bravo-Uretaand Rieger (1990) examine New England andNew York farm efficiency using four productionfrontier methods. The result of their analysisindicates that, while large differences existbetween estimated average firm efficiency ratios,all four sets of efficiency ratios are highlycorrelated within two time periods.

Kalaitzandonakes et at. (1992) examined therelationship between firm size and technicalefficiency on a sample of Missouri grain farmsusing three production frontiers. There arestrong differences between estimated averageefficiency ratios from the three methods. Byrneset al. (1987), using a nonparametric radial outputefficiency measure, fmd that south-central Illinoisgrain farms are producing only four percentbelow their efficient levels. However, AIy et al.

(1987) and Neff et al. and Hornbaker (1991)using a deterministic parametric frontier, findthat farms are producing at approximately 60-65percent of their efficiency level. Finally,Grabowski et al. (1990) employing a stochasticparametric frontier, find that a sample of Illinoisgrain farms are producing at 82 percent of theirefficient levels.

Given the result of previous studies, thepurpose of this paper is to provide a comparisonof the most commonly used frontier methodsutilizing four production frontier methods,namely:

a. Deterministic Parametric Frontier (COLS)b. Linear Programming Parametric Frontier

(LP)c. Nonparametric Frontier ( PAR), andd. Stochastic Parametric Frontier (SPF)

This paper proceeds as follows. The nextsection focuses on the methodology that areused in this study. Section three presents thedata and estimation followed by the empiricalresults. The last section concludes the study withthe implications of the findings.

METHODOLOGYDeterministic Parametric Frontier

Let y represent the output of a firm and let xdenotes a vector of input utilized in the

104 PertanikaJ. Soc. Sci. & Hum. Vol. 7 No.2 1999

Technical Efficiency Estimates for Sarawak Pepper Farming

n

Min 2u ii-:=1

To solve this using LP method, LU; is

expressed as a linear function of a and X. .The production function in (I) is the~ summ~~

over i and LUi is solved, that is

Only efficient farms satisfY the strict equality.In order to determine the unique vector awhich satisfy (4), Timmer (1970) suggest~minimizing the linear sum of residuals ratherthan minimized the linear sum of squareresiduals since the latter accentuates the impactof extreme observation. Thus the problem is tofmd a

g, in order to:

(5)G

"'aX. ~y.LJ g Ig 1

g=O

st

(1)

From the output relationship estimated byOrdinary Least Squares (OLS), the frontierproduction function is derived by a methodcalled Corrected Ordinary Least Squares (COLS) .It has been shown that the COLS estimates givecoefficients which are unbiased and consistent(Green, 1980). The procedure involves estimatingthe individual specific error terms from theproduction function, and revising the interceptby the magnitude of the largest error term. Theresults in output magnification not only at thatpoint but over the entire production surface.Thus, the frontier function is given by

wherea a constant and~ a vector of slope coefficients.

production of y. The deterministic parametricfrontier is estimated assuming a conventionalCobb-Douglas production technology:

Y* = a* II X~ e u (2) (6)

The technical efficiency measure of anindividual firm is the ratio of actual output Y, topotential output, Y*

(8)

Having estimated the production frontier,the efficiency ratings are calculated for eachfarm in each year as Y/Y'. Thus, that LP measureof technical efficien~y 'for farm i is given byexponential of these ratio, that is

ao + a,X ln+ a 2X 2n + +acXCn

~ X,a ~ 0

g

Min ao + a j Xl + a 2 X 2 + +acXcst

(7)

However, for any data set, the last term onthe RHS of (6) is a constant, so it can beremoved. What remains becomes the objectivefunction. Timmer (1970) suggests that theproblem is computationally simpler when theobjective function is divided by the number ofobservations. Thus, the LP problem is to finda g, in order to:

(4)

(3)

1=1,2, ... , n

Y' + u.the fr~ntier estimate of X, andthe residual of farm i

TE = Y/Y* s 1

where

XX'u

i

Linear Programming Parametric Frontier

A further measure of technical efficiency can beestimated using linear programming methods(Aigner and Chu, 1968; Timmer, 1970, 1971).This approach differs from the DeterministicParametric Frontiers in that the assumption oflinear homogeneity is relaxed at a cost ofspecifying a functional form for the productionfunction. Again, the Cobb-Douglas specificationis used. Using Eq. (1), assume that thedisturbance terms are constrained to be onesided, that is, u; s 0 so that the function is afrontier one. For an efficient frontier, this shouldbe estimated so that:

G"'a X . =y' ~y.L-igglJ IgoO

PertanikaJ. Soc. Sci. & Hum. Vol. 7 No. 21999 105


T = {(x,y): zy;;" y, zX s x, LZi

= 1, Z E R+l (9)

Technical efficiency i estimated by solvingthe following linear programming for each farmi:

Nonpammetric Frontier

Nonparametric frontiers were originally proposedby Farrell (1957). The radial output measure oftechnical efficiency is estimated by assuming anonparametric production technology (T) withstrong disposable output and inputs, and nonconstant return to scale:

(13)

(12)

output of ith farmsa vector of inputs,a vector of parameters, andan error terms

E. = v. - u., , ,

The error component vi is assumed to bedistributed normally with mean zero and variance0v

2(Vi - N (0,ov2)) and account for variability in

the frontier due to random shocks or noise.The error component ui is assumed to bedistributed half-normally (ui-IN(O, ,oJ) andassumed to capture firm' inefficiency, that isdeviation from the stochastic frontier. Equation(4) is estimated using maximum likelihood. Thetechnical efficiency related to the stochasticproduction frontier is

The stochastic frontier is also called composederror model, because it postulates that the errorterms (i is composed of two independent errorcomponent:

where

\XiB;

(10)

Max e;st

zy ;;" e,Y;zX ;;" Xi

Lz; 1

wherex a (n x 1) vector of inputsy a (m x 1) vector of outputsk the number of farmsX the (n x m) matrix of inputsy the corresponding (n x k) matrix of

outputs, andZ the intensity with which any activity

(x,y) is utilized.

For the single-output nonparametricefficiency measure used here, there is one outputconstraint in (10). There are six input constraintfor the measures. The solution to eachprogramming, e, represent the ratio of eachfarm frontier output to observed output. The

efficiency ratio, TE= ~ , indicates the percentage

(TE x 100) of output achieved by each firm. Aprimary difference between nonparametric andparametric production frontiers is that the formerdoes not assume any parametric form. Hence,instead of attempting to fit a regression surfacethrough the center of the data, nonparametricprocedures lay a piecewise linear surface on topof the observation (Kalaitzandonakes et at. 1992).

Stochastic Parametric Frontier

Aigner et ai., (1977) and Meeusen and Van denBroeck (1977) have specified and estimated astochastic production frontier which can bewritten as:

(11)

capture by the one sided error component u i ;;" 0Qondrow et aI., 1992).

DATA AND ESTIMATION

A cross section of 159 sample Sarawak pepperfarms was used to estimate the productionfrontier models discussed in the previous section.Our empirical model consists of a single equationproduction function, which is justified byinvoking expected profit maximization. TheCobb-Douglas functional form was chosen, ashas been the practice in most published efficiencystudies, because of its well-known advantages.The specific model estimated is:

In Q = Bo+ B] In Xl + B2 In X2

+B3

InX3

+B4 InX4 (14)+ Bs In Xs + E

whereQ = pepper production (kg/year)Xl = the fertilizer used (kg/year)X

2= the weedicide used (It/year)

X3

= the chemical used (It/year)



X4

= labour (manday/year)Xs = number of vines cultivated(l. = parameter to be estimated, i =1,2,,51-'0E = disturbance terms

As the first step, Ordinary Least Square(OLS) is applied for estimation, yielding bestlinear-unbiased estimates of productioncoefficients. The scale parameter estimates isthen corrected by shifting the function until noresiduals is positive and one is zero. In theapplication of the LP deterministic parametricfrontier, equations (7) are used to estimate theparameters.

The nonparametric model derived theefficiency of each farm by comparing its observeduse of inputs and produced output relative to allother farms. In the application to the Sarawakpepper farms, 159 farms observations of fiveinputs and single output are assembled.Therefore, there are five equations for inputconstraints and one additional constraint thatthe element of the intensity vector sum to one

(Lz = 1). Since 159 farms are present, a series of

159 such linear programming must be solved todetermine the technical efficiency of each farm.

Estimation of parameters of stochasticfrontier as well as the consequential diagnostics

and statistical test was accomplished by using themaximum likelihood method (Greene, 1992).

RESULTS AND DISCUSSION

Table 1 presents COLS, LP and stochasticestimates of the production function parameters.The adjusted R2 indicates that the fittedregression explain 53.75 percent of the variationin pepper production for COLS model. It isinteresting to note that farmers were operatingat almost constant return to scale as indicated bythe sum of the estimated coefficient. Theregression coefficients for all the variables arepositive and significant at 1 percent level.However, in the case of LP model, no standarderror and R2 can be calculated, but the interceptestimate is higher than the COLS method.

The corresponding stochastic and COLSestimates are quite similar in term of signs. Thelevels of significant for the correspondingcoefficients are largely the same with theexception of the case for chemical. The COLSestimate of the intercept is smaller than thestochastic estimate. This confirms that the averageproduction function (traced by the COLSestimates) lies below the stochastic productionfunction reached by maximum likelihoodestimates. The variance ratio parameter

TABLE 1Estimates of production function

Fertilizer

Weedicide

Chemical

Labor

No. of Vine

Constant

R2-AD]a2

vo'2.

u

Log-Likelihood

DeterministicParametric (COLS)

0.2364(7.415)a0.1151

(4.680)'0.2508

(2.827)'0.2048

(2.995)a0.1666

(5.527)'1.1195

(0.2603)0.5375

LP-DeterministicParametric

0.1619

0.1489

0.2391

0.2774

0.1993

1.4066

StochasticParametric (SPF)

0.31160(6.234)'0.0881

(2.138)'0.2232

(1.458)0.24941

(1.984)b0.25180

(4.981)'2.0513

(1.661)b

0.10680.0671

-63.7464

Note: Figures in parentheses are t-statisticsa Significant at 1% levelb Significant at 10% level

Pertanika.J. Soc. Sci. & Hum. Vol. 7 No.2 1999 107


( A = :: ) , a measure to indicate the extent of

total variation that is due to differences inproduction efficiency, is found to be 0.78. Thissuggests that a high portion of the differencesbetween farmers' realized production and themaximum possible productions are due tofarming practices rather than random behaviour.

Table 2 presents the results of the efficiencyanalyses for four frontier models. At first glance,the results show considerable variability in thevalue of mean technical efficiency acrossmethods. On average, the mean efficiency ratiosof the sample farms are high, over 80 percentfor SPF measures. The NPAR measure indicatesthat the pepper farms are almost 80 percentefficient, which is about 1 - 2 percent lower thanaverage measures for the SPF model. The COLSfrontier method has the lowest average efficiencyratio for the pepper farms. The COLS measureindicates that farms are approximately 62 percentefficient on average, about 3 - 4 percent lowerthan the average measures for the LP method.Both measures are about 20 - 22 percent lowerthan the average measure for the NPAR and SPFmodels. Efficiency ratios from the SPF modelare higher than the COLS model becausemodeling the error term in SPF as a compositeof random error and inefficiency, rather thansolely as inefficiency (Neff et ai., 1993).

The nonparametric model tends to result inhigher average efficiency measures than theparametric model (except for the SPF model).A significant reason for this is that the NPAR

model analyses construct a different frontier forevery sample farm. This result is consistent withNeff et at. (1993) where the PAR model is apiecewise-linear, not a smooth function as in theCOLS and SPF models.

The standard deviation for SPF model is thesmallest compared to other three models.Consequently, the SPF model provides farmefficiency estimates with much lower variabilitythan any of the other methods. For the SPFmodel, the technical inefficiency of each farm isa point estimate, that is, the mean of theconditional distributions of each farm'sinefficiency error component (u) given its totalerror term (E). The mean for the conditional~is~ibutions (uiIE) of the sample farms are verysln:I1ar resulting in low variability in the efficiencyrauos.

Table 2 and Fig. 2 represent distributions offarm efficiency ratios. The COLS and LP modelsis almost normally distributed. Approximatelyonly 8 percent of the farms are very efficient(ER;" 90 percent) and 28 percent are inefficient(ER :S 50 percent) for COLS model. For LPmodels, approximately 13 percent of the farmsare very efficient and 24 percent are inefficient.The COLS model, which is parametric, resultsin only one farm being on the frontier (ER = 1)and two farms for LP models.

The distribution of the NPAR model isskewed to the left. This is primarily due to alarge number of efficient, or very efficient (ER ;"90%), farms associated with the nonparametricfrontiers. The results indicate that a large number

TABLE 2Frequency of efficiency ratio of pepper farming in Sarawak

Deterministic LP Parametric Non-Parametric StochasticParametric (COLS) (LP) (NPAR) Parametric (SPF)

31 - 40 12 ( 7.5) 11 ( 6.9)41 - 50 33 (20.8) 28 (17.6) 13 ( 8.2)51 - 60 45 (28.3) 40 (25.2) 17 (10.7) 1 ( 0.6)61 - 70 23 (14.5) 26 (16.4) 25 (15.7) 2 ( 1.3)71 - 80 13 ( 8.2) 17 (10.7) 17 (10.7) 50 (31.4)81 - 90 20 (12.6) 16 (10.1) 20 (12.6) 104 (65.4)91 - 100 13 ( 8.2) 21 (13.2) 67 (42.1) 2 ( 1.3)Minimum 0.3398 0.3605 0.4106 0.5878Maximum 1.0000 1.0000 1.0000 0.9064Average 0.6162 0.6415 0.7999 0.8168StandardDeviation 0.1712 0.1823 0.1923 0.0536

Note: Figures in parenthesis represent percentage of total sample



91-10081-9071-8051-6041-50 61-70

EfficIency Ratio

• Deterministic Parametric (COlS). Non- Parametric (NPAR)[J lP Parametric (lP) rl Stochastic Parametric (SPF)

70

60

50 fr'"

-c 40ell0...ell 30a.

20

10

031-40

Fig. 2. Distribution of efficiency ratio

of farms being on the frontier. For the NPARmodel, there are 55 farms with ER = 1. In part,this is a result of piecewise-linear manner inwhich the nonparametric frontiers areconstructed where each farm observation has itsown frontier.

The distribution of the efficiency ratio forthe SPF model is in contrast to the other threemeasures. Over 65 percent of the sample farmsare concentrated in the 80 - 90 percent efficiencyregion. On average, it appears that none of thesample farms in the SPF model have efficiencylevel less than 50 percent and also none areperfectly efficient. This is because the frontier isstochastic, and a portion of the total error isattributable to random behaviour (Neff et ai.,1993).

Table 3 presents summary statistics of thedifferences (DER) between the efficiency ratiosestimated by the four frontier methods. A large

number posItIve differences indicate that, ingeneral, the efficiency ratio of four models areranked as SPF > NPAR > LP > COLS. There arelarge differences between the efficiency ratios ofthe COLS, LP and NPAR models. NPARefficiency ratios are 16 percent and 19 percenthigher on average, respectively, than those ofCOLS and LP methods.

CONCLUSION

The purpose of this paper is to compare theresults derived from alternative productionfrontier estimation methods. The Cobb-Douglasfunctional form was used to evaluate the fourmethods that have been frequently employed inthe literature, on a sample of 159 pepper farmsin Sarawak.

In general, all the four models indicate thatSarawak pepper farms are producing at 60 - 80percent efficiency ratio. However, the study

TABLE 3Summary statistics of difference in efficiency ratio (DER) between four frontier models

COLS- COLS- COLS- LP- LP- NPAR-LP NPAR SPF NPAR SPF SPF

Der> 0 37 1 20 0 30 74Der 2: 0 122 158 139 159 129 85

Difference in Efficiency RatioAverage -0.03 -0.18 -0.20 -0.16 -0.18 -0.02Minimum -0.15 -0.59 -0.42 -0.61 -0.45 -0.36Maximum 0.11 0.01 0.14 0.00 0.14 0.41

PertanikaJ. Soc. Sci. & Hum. Vol. 7 No.2 1999 109


revealed that systematic differences m theefficiency measures are attributable to themethod used. Differences also exist in thedistribution of efficiency measures and therelative rankings of the farms by various models.The distributions of the COLS and LP measuresare widely dispersed and more normallydistributed. In contrast, the distribution ofefficiency ratios from the stochastic parametricmethod is highly concentrated around 70 - 90percent efficiency rate. This is in part due to theneed to estimate inefficiency using the Jondrowet al. (1992) decomposition. However, in thecase of nonparametric frontier, the resultsindicate that 35 percent of the sample farms areperfectly efficient (ER = 1). This is because thefrontier is more flexible; that is, it is a piecewiselinear instead of continuous, functional form;and it constructs a different frontier for eachobservation.

In summary, the results indicate that frontierproduction functions proved significant incomputing efficiency level in pepper production.The results can assist those involved in theindustry's decision making to formulate strategyin abating inefficiency in order to enhanceproductivity. For example, a low level of technicalefficiency indicates that increasing productionwould require new innovations or high-techfarming system. However, the absolute level, thedistribution and the relative ranking of farmefficiency as shown in this study are influencedby the method employed. Thus, before anyremedies can be suggested, the precision ofpredictors for individual technical efficiencyshould be carefully considered.

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ALY, H.Y., K. BALBASE, R GRABOWSKI, and S. KRAIT.1987. The technical efficiency of Illinois grainfarms: an application of a Ray-homotheticproduction function. Southern J. Agric. Econ.19: 69-78.

BRAVO-URETA, B.E. and L. RIEGER. 1990. Alternativeproduction frontier methodologies and dairyfarm efficiencies. J. Agric. Econ. 41: 215-226.

BYRNES, P. R FARE and S. GRASSKOPF. 1987. Technicalefficiency and Size: The case of Illinois Grainfarrns. Euro. Rev. of Agric. Econ. 14: 367-38l.

FARRELL, MJ. 1957. The measurement of productiveefficiency. J. Royal Statistic Soc. Series. A, 120:253-290.

FORSUND, F.R., CA.K. LOVELL, and P. SCHMIDT. 1980.A survey of frontier production functions andof their relationship to efficiency measurement.J. Econ. 13: 5-25.

GRABOWSKI, R A. KRAIT, C. PASURKA, and H.Y. My.1990. A Ray-Homothetic and efficiency: grainfarms in southern Illinois. Euro. Rev. of Agric.Econ. 17(4): 435-448.

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KALArTZANDONAKES, N.G., S. Wu, and]. MA. 1992.The relationship between technical efficiencyand farm size revisted. J. Agric. Econ. 40: 427442.

MEEUSEN, W. and]. VAn DEN BROECK. 1977. Efficiencyestimation from Cobb-Douglas productionfunctions with composed error. Int. Econ. Rev.18: 435-444.

NEFF, D.L., P. GARCIA. and R.H. HONBAKER. 1991.Efficiency measure using the Ray-Homotheticfunction: a multi period analysis. J Agric. Econ.23: 113-121.

NEFF, D.L., P. GARCIA. and C.H. NELSON. 1993.Technical efficiency: a comparision ofproduction frontier methods. J Agric. Econ.44: 479-489.

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(Received: 30 November 1995)

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technical efficiency estimates for sarawak pepper farming...

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