03 Joscm Vol2 Number 2 31

8/3/2019 03 Joscm Vol2 Number 2 31

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Cobb-Douas, Transo Stocastic Production Function

and Data Enveopment Anasis in Tota FactorProductivit in Braziian Aribusiness

Paul Dutra CnstantinUniversidade Presbiteriana Mackenzie

[email protected]

Digenes Leiva MartinUniversidade Presbiteriana Mackenzie

[email protected]

Edard Bernard Bastiaan de Rivera Y RiveraUniversidade Presbiteriana Mackenzie

[email protected]; [email protected]

ABSTRACT: The bjective f this paper is t apply a Cbb-Duglas, Translg Stchastic Prductin Functin and DataEnvelopment Analysis in order to estimate ineciencies over time as well as respective TFP (Total Factor Productivity)surces fr main Brazilian grain crps - namely, rice, beans, maize, sybeans and heat - thrughut the mst recentdata available cmprising the perid 2001-2006. The results indicate that, althugh psitive changes exist in TFP frthe sample analyzed, a decline in the use f technlgy has been evidenced fr all grain crps in hich it is bserved ahistrical dnfall in the use f inputs in Brazilian agriculture.

KEYwoRDS: Ttal Factr Prductivity, Stchastic Frntier, Data Envelpment Analysis.

1. INTRODUCTION

Not all producers are technically ecient. As op-psed t cnventinal micrecnmic thery, suchstatement implies that nt all prducers are able tutilize the minimum quantity f required inputsin rder t prduce the desired quantity f utputgiven the available technlgy. Similarly, nt all pr-ducers are able t minimize necessary csts fr the

intended prductin f utputs.Frm a theretical pint f vie, prducers d nt al-ays ptimize their prductin functins. The pr-ductin frntier characterizes the minimum numberf necessary cmbinatins f inputs fr the prduc-tin f diverse prducts, r the maximum utputith varius input cmbinatins and a given tech-nlgy. Prducers perating abve the prductinfrontier are considered technically ecient, whilethse h perate under the prductin frntier aredenoted technically inecient.

ThE FlAgShIP RESEARCh JOURNAl OF INTERNATIONAl CONFERENCEOF ThE PRODUCTION AND OPERATIONS MANAgEMENT SOCIETyVolume 2 Number 2 July - December 2009

20

The Stchastic Frntier Analysis SFA is an analyti-cal approach that utilizes econometric (parametric)techniques hse mdels f prductin recgnizetechnical ineciency and the fact that random shocksbeyond producers control may aect the product.Dierently from non-parametric approaches that as-sume deterministic frntiers, SFA alls fr devia-tins frm the frntier, hse errr can be decm-psed fr adequate distinctin beteen technical

eciency and random shocks (e.g. labor or capitalperformance variations).

By the applicatin f nn-parametric methds asData Envelpment Analysis DEA, the Malmquistindex is calculated by distance functins btained bymathematical prgramming and alls fr the ab-sence f price infrmatin, utilizing physical quan-tities f multiple inputs and prducts instead. Themain t cmpnents f the underlying index aretechnical change (innovation) and eciency change(catching up eect towards the frontier).


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Constantin, P. D. Martin, L. M. Rivera, E. B. B. R.:Cobb-Douglas, Translog Stochastic Production Function and Data Envelopment...Journal of Operations and Supply Chain Management 2 (2), pp 20 - 34, C International Conference of the Production and Operations Management Society 21

The bjective f this paper is t apply the Stchas-tic Frntier Analysis technique in rder t estimateincrease or decrease in ineciencies through time,as ell as the linear prgramming methd Data En-velpment Analysis, namely the Malmquist index,fr the analysis f change in TFP (Total Factor Pro-

ductivity)in main Brazilian grain crps rice, beans,maize, sybeans and heat thrughut the 2001-2006 perid.

Amng bserved results, even thugh there havebeen psitive changes in main Brazilian grain crps,there have been a decline in the cmpnent refer-ring t technlgical innvatins fr all Braziliangrain crps analyzed beteen the 2005/2006 peridin hich it is bserved a general dnfall in inputusage in agriculture.

2. ThEORETICAl FRAMEWORK

2.1 Stocastic Frontier Anasis - SFA

In the presence of ineciencies, the Stochastic FrontierAnalysis SFA emerges as a theretical and practicalframerk, hse bjective is t cntribute fr thedenition and estimation of production frontiers. SFAhas been developed from remote inuences but theliterature that directly inuenced the development ofSFA has been the theretical framerk abut pr-duction eciency beginning in the decade of 1950 by

Koopmans (1951), Debreu (1951) and Shephard (1953).Farrell (1957) was the rst to measure production e-ciency empirically. The use f linear prgramming byFarrell inuenced research by Boles (1966), Bressler(1966), Seitz (1966) and Sitorus (1966) and eventu-ally the develpment f Data Envelpment Analysis(DEA) by Charnes, Coopers and Rhodes (1978). Theinuence from Farrell is also denite for the works byAigner and Chu (1968), Seitz (1971), Timmer (1971),Afriat (1972) and Richmond (1974) direct collabora-trs fr the SFA develpment.

This parametric methd f stchastic frntier cn-siders prductin frntier as a randm shck. Dif-ferently frm a nn-parametric methd such as DEAthat assumes a deterministic frntier, the stchasticfrntier alls fr deviatins frm the frntier trepresent both ineciency and an inevitable statis-tic nise hich intends t be a clser apprach treality given that bservatins nrmally invlve arandm alk.

SFA has its rigins in t papers: Aigner, Lvelland Schmidt (1977) and Meeusen e van den Broeck

(1977), followed by the works by Baese and Corra(1977). These three original works represent, in thecontext of production frontier, the error term denedin a structurally cmpsed manner. Since then, theSFA has been develped by several cllabratrs:Schmidt and Lovell (1979), Jondrow et al. (1982),

Greene (1980), Stevenson (1980), Lee (1983), Koopand Diewert (1982), Pi and Lee (1981), Schmidt andSickles (1984), Cornwell, Schmidt and Sickles (1990),Kumbhakar (1990), Baese and Coelli (1992), amongther researchers.

The mdels f stchastic prductin frntier ad-dress technical eciency and recognize the factthat randm shcks beynd the cntrl f prduc-ers may aect the production output. Therefore, inthese models, the impact of random shocks (as laboror capital performance) on the product can be sepa-

rated from the impact of technical eciency varia-tin. These mdels ere simultaneusly intrducedby Aigner, Lovell and Schmidt (1977) and Meeusenand van den Broeck (1977).

This paper has flled the dminant functinalspecication in literature based on the works by Bet-tese and Coelli (1992, 1995), in which it is formalizedtechnical ineciency in the production function ofstchastic frntier fr panel data. Thus, cnsider theflling prductin functin f a given state i:

r

sectrs and

years

here ity is the vectr representing prduced quan-

tities by the unit f prductin in perid ;is the vectr f inputs used by the unit f prduc-

tin in perid ; is the vector of coecientsto be used that dene the production technology.

The terms and are vectrs representing dis-tinct error components. The rst term refers to the ran-dm part f errr, ith nrmal distributin, indepen-dent and identically distributed (iid), truncated in zero

and variance [v ~iid N(0, )]. The secondterm concerns the part relating to technical ineciency,cnstituting a deviatin in relatin t the prductinfrontier (which can be inferred by negative sign and by


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Constantin, P. D. Martin, L. M. Rivera, E. B. B. R.:Cobb-Douglas, Translog Stochastic Production Function and Data Envelopment...Journal of Operations and Supply Chain Management 2 (2), pp 20 - 34, C International Conference of the Production and Operations Management Society22

restrictin ). They are nonnegative ran-dm variables ith nrmal truncated distributin, that

is, nn-null mean [u ~N+ (m, 2us )].

The OLS (Ordinary Least Squares) method providesa simple test for the identication of the presenceof technical ineciency in data. If ,then . Thus, the errr term is symmet-ric and data do not evidence technical ineciency.Hever, if , then the distributinf is negatively symmetricand evidences of technical ineciency in data exist.Thus, the term quanties technical inecien-cy or the distance in relation to the eciency frontier.The most ecient estimate presents value 0 for

. This suggests that the presence of technical ine-ciency can be tested directly by the residuals f oLS.

Consider technical ineciency as time-variant

when is psitive, the value inside the brackets fthe exponential term will become non-negative and (

ill nt besmaller than unity. This is the case in hich

. In other words, technical ineciency willhave decreasing eects through time (positive ef-

fect in technical eciency over time). In case is

negative, ineciency will be increasing through time(also dened as persistent inecieRiverancy).

2.2. Data Enveopment Anasis - DEA

A productively ecient rm is the one not able toincrease its prductin unless sme f its inputs arealso increased. By the Malmquist index, such rmachieves an eciency score of 1. Similarly, a produc-tively inecient rm obtains an eciency punctua-tin smaller than 1.

Introduced by Caves et al. (1982) in its empirical us-age, the Malmquist index d nt require csts r in-cme, being capable f measuring increase in TFP ina scenari f multiple prducts. Fr the Malmquistindex denition, we assume that for each period of

time, prductin technlgy

mdels the transfrmatin f inputs

int prducts .

(3)

Fre et al. (1994) dene the output distance function

at time as

(4)

Thus, the distance functin in relatin t t dif-ferent perids measure the maximum prprtinal

change required in prductin t turn

feasible in relatin t technlgy in pe-

rid . Caves, Christensen e Diewert (CCD) (1982)dene Malmquist productivity as

(5)

In this frmulatin, technlgy at time is thereference technology. Alternatively, Fre et al. (1994)dene a Malmquist index based on period

as

(6)

In rder t avid an arbitrary benchmark, Fre etal. (1994) specify the Malmquist index for changes

in prductivity as the gemetric mean f bth CCDtype Malmquist indexes:

(7)

An equivalent frm t express this index:

(8)

In the study cncerning industrialized cuntries,Fre et al. (1994) observe that this decomposition al-ls fr a measure in hich ne distinctin existsbetween technical eciency components (catching-up) and technology change (innovation), given thatprevius rks did nt distinguish beteen these


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t cmpnents.

The ratis inside the brackets measure changes in tech-

nlgy dislcatins t input levels and, respectively. Thus, changes in technlgy is measuredas the gemetric mean f these t cmpnents. The

terms out of the brackets measure technical eciencyrelative t and , capturing changes ineciency over time, that is, whether production be-comes closer (catching up eect) or more distant fromthe frntier.

observe that if and

(i.e., no input and product change betweenperiods), the productivity index do not signalize anychange: . Imprvements inprductivity result in Malmquist indexes greater thanunity. Similarly, perfrmance deteriratin ver time is

assciated ith a Malmquist index smaller than unity.Besides, imprvements in any f the Malmquist indexcmpnents are als assciated ith values greaterthan unity f these cmpnents; and deteriratin isassciated ith values smaller than unity.

Finally, Fre et al. (1994) highlight that, while the prod-uct of the components of eciency change and tech-nical change must, by denition, equal the Malmquistindex, these cmpnents may be mving in ppsitedirectins. Fr instance, a Malmquist index greaterthan unity, say 1.25 (which signalizes productivity

gain), could have a component of eciency changesmaller than 1 (e.g. 0.5) and a change in technologycomponent greater than unity (e.g., 2,5).

Alternatively, Alam (2001) expresses the Malmquistindex in terms f distances thrughut the y-axis,based n Figure 1:

Fiure 1: Mamquist Index

Source: Adapted by the authors from Alam (2001).

(9)

Consider the case of a rm in perid

represented by . Given that it is l-

cated under , this rm is not ecient and itsproductive ineciency is measured by the ratio

. Similarly, the same rm in t+1 , dented by

is ecient in relation tothe frntier and its ineciency measure

is given by .

Given that this index captures the prductivity dy-namics by the incrpratin f data frm t dif-

ferent adjacent perids, reects change in

relative eciency, while reects changes

in technlgy beteen perids and .As fr the index and its cmpnents, values smaller

than 1 indicate a decline in productivity (regres-sion), while values greater than 1 indicate growth

(progress). For the rm in the example, bthcomponents exceed 1. In terms of technical ecien-cy, the rm moved to a point closer to the contempo -rary relevant frntier, indicating that the prductinfor this rm is converging to the frontier. In termsf technlgical change, the frntier, measured at

levels f inputs and , mved be-

teen perids and (

(ALAM, 2001).

3. METhODOlOgy

From LSPA (Systematic Survey of Agricultural Pro-duction) of January 2007 released by the BrazilianInstitute of Geography and Statistics (IBGE), datahas been gathered fr the main Brazilian grain crps rice, beans, maize and heat. Thus, btained pr-ductions have been analyzed for each culture (out-puts), as well as harvested area in acres for each crop(inputs) annually.


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Additionally, from PAM (Municipal Agriculture Production) and the statistics available at the Ministry of Ag-riculture, data has been gathered on total quantity (in ton.) produced, harvested area (acres), agricultural credit(in Brazilian Real) and agricultural limestone (in ton.) for the period 2001 to 2006 for the 26 States of the Federa-tin and the Federal District, alling fr the creatin f reginal dummies fr the cmparative analysis f ttalfactr prductivity.

Initially, data has been analyzed based n the stchastic frntier thery in rder t verify gains r lsses in ef-

ciencies over time, expressed by the component and the estimated parameters f variables that explain

technical ineciency. Considering technical ineciency

as varying thrugh time, if is psitive, the value inside the brackets f the expnential term ill becme

nnnegative and ill nt be greater than 1. This is the case in hich. In other words, technical ineciency will be decreasing over time (positive eect of technical ef-

ciency through time). If is negative, ineciency will be increasing. In case is null, it is bservedtechnical ineciency that does not vary over time (also referred as persistent ineciency).

In relation to Data Envelopment Analysis and the Malmquist index, Fre et al. (1994) discuss the usage of theVRS approach in the Malmquist index calculation. By calculating change in eciency in relation to the VRSfrontier, it is obtained the denominated change in eciency and measured changes in production scale by theratio between change in eciency and change in pure eciency. Thus, the component change in eciency(or technical eciency) calculated in relation to technology with CRS can be decomposed in a component ofchange in pure eciency (PEC, calculated in relation to the technology with VRS) and, in a component of changeof scale eciency (SEC), which represents changes in deviations between the CRS and VRS technologies.

Thus,

here

which can be re-wrien in the following form:

The decomposition of Malmquist index assists in the determination of eciency or ineciency sources in a

rm. indicates technical prgress. means the rm is approxi-

mating tards ptimal scale in .

4. RESUlTS AND DISCUSSION

4.1 Stocastic Frontier Anasis for Braziian Aricuture: Cobb-Douas Production Function

The results related t the estimatin f the stchas-tic frntier analysis accrding t a Cbb-Duglasprductin functin is presented in Table 1. In thecase of a Cobb-Douglas model, the signicant vari-ables ere harvested area, agriculture credit andlimestne all assuming expected signs. The LR(Likelihood Ratio) statistic, which is a chi-square (

distributin under the null hypthesisthat there has not been eects of technical eciency,presents signicant value to the 1% level, indicatingeects of technical ineciency in the model.

The greatest elasticity bserved is that f harvestedarea. This indicates the intense relatinship that ex-ists beteen prductin and harvested area, inde-pendently f the utilizatin f ther factrs that, cet-eris paribus, uld cntribute fr prductivity. Thecredit variable reveals the secnd majr elasticity,conrming the importance of agriculture credit tocver csts and particularly, t execute investmentshich respnds fr the greatest share f the dataanalyzed. As expected, assuming psitive and infe-rir elasticity in relatin t the ther relevant factrs,


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limestne cntributes fr prductivity by crrecting sle acidity, hich assumes a maximizing rle fr theptential f prductivity already established by the ther factrs.

The estimate f parameter , which measures the variability of the two sources of error (white noise distur-bance and unilateral error), reached the level of 0.9469. This result means that about 95% of total variance ofcomposed error of the production function is explained by the variance of the technical ineciency term. This

represents the importance of incorporating technical ineciency in production function.

The term relative to technical ineciency assumes a temporal paern of behavior represented by the sign.In case this term is positive (negative), technical ineciency will be decreasing (increasing) in time. If it assumesa null value, it is considered that technical ineciency does not vary in time - also called persistent ineciency.In the analysis, the term assumes negative value, which indicates that technical ineciency in Brazilian agricul-ture, thugh nt predminant, is increasing in time frm 2000 t 2005.

Thus, the punctual reduction of ineciency, which includes the concession of costs credit for income main-tenance against uctuations in prices and exchange rates, as well as investment credit for capital acquisitionsuch as tractors and harvesters will certainly avoid the persistence of increasing ineciency path in Brazilianagricultural prductivity.

Tabe 1 Cobb-Douas Production Function

Num. f bs = 162 obs. by State: min = 6

Num. of States = 27 Avg: 6

Max: 6

wald 2)24(c = 645,38

Log likelihood = 15,419691Prb >

2c = 0,0000

lny Cef. Std. Errr z P>z 95% Conf. Interval

ler limit upper limit

)(ln reaharvestedaAb1.0665 0.0536 19.87 *** 0.9613 3.4805

)(ln creditCb0.8882 0.0395 2.25 *** 0,0113 -1.2771

)(lndefensivesDb0.0154 0.0302 0.51 -0.0438 0.8018

)lim(ln estoneRb0.0721 0.7372 4.18 *** 0.0382 2.5952

0b-1.2327 0.6986 -1.76 * -2.6021 0.1366

m 1.3621 0.2784 4.89 *** 0.8164 1.9078

h -0.0123 0.0077 -1.60 -0.0274 0.0028

g 0.9469 0.0185 0.8964 0.9735

2

us0.4073 0.1391 0.1347 0.6800

2

vs0.0228 0.0028 0.0172 0.0283

Surce: Research results btained frm gathered PAM and Ministry f Agriculture data fr the prpsed

stchastic frntier mdel.

Note: *** signicant to the 1% level; ** signicant to the 5% level; * signicant to the 10% level.


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4.2 Stocastic Frontier Anasis for Braziian Ari-

cuture: Transo Production Function

Assuming a logarithmic transcendental (translog)technlgy, the parameters estimates f the prduc-tion frontier and the technical ineciency compo-

nent are presented in Table 2. The statistically sig-nicant parameters at the level of 5% are essentiallyrelated t harvested area and agricultural credit, aswell as the measures of regional technical inecien-cy expressed by dummy variables. The LR (Likeli-hood Ratio) statistic presents signicant value at 1%level, indicating eects of technical ineciency inthe mdel.

Analyzing the sample n the basis f stchastic frn-tier theory for the verication of gains or losses of

eciencies through time, it is observed that the

component assumes negative sign and is signicantat 5% level. Thus, technical ineciency is increasingver time fr the analyzed sample. It is imprtant

t emphasize that is unique fr the analyzedsample. Thus, this cmpnent des nt reveal pr-ductivity specicities for each state.

The coecient for the mean of the error component

relative to ineciency, , is nt statistically signif-icant, indicating that the semi-nrmal distributin ismre apprpriate in relatin t the nrmal truncated

distribution ( ).

The psitive sign f parameter indicates thatthe ccurrence f technical prgress. The indicatr

of technical ineciency, , presents apprximatedvalue of 0,90. This result indicates that 90% of totalcmpsed errr variance f the prductin functin isexplained by the variance of the technical ineciencyterm. This reveals the imprtance t incrprate tech-

nical ineciency in the production function.

In relatin t the dummy variables parameters, theyare all statistically signicant to the 5% level. By hav-ing the Nrtheast regin as reference fr presentinga larger number of observations, it is veried thatall the other regions are technically less ecient inrelatin t the reference regin. Thus, by classifyingaccording to the degree of increasing ineciency,Nrth regin is flled by Sutheast regin, Suthand Center-west, respectively.

The coecients and indicate that theneutral part of technical progress has a positive eectover production. The signs of the coecients , , and indicate, respectivelythat the nn neutral part f technical prgress mvesinversely ith area, credit, defensives and accrd-ingly ith limestne. Hever, these parametersare not signicant at the 5% level. That is, technicalprgress tends t diminish the usage f harvestedarea, agricultural credit, defensives and, n the th-er hand, is assciated ith the increase f limestneutilizatin.

Table 2 Time-Varying Ineciency Model (B&C, 1992)

Num. f bs = 162 obs. by State: min = 6

Num. of States = 27 Avg: 6

Max: 6

wald 2)24(c = 3638,03

Log likelihood = 46,578465Prb >

2c = 0,0000

lny Cef. Std. Errr z P>z 95% Conf. Interval

ler limit upper limit

)(ttb0,5324 0,2963 1,80 * -0,0483 1,1131

2)2/1( tttb0,0094 0,0175 0,53 -0,0250 0,0437

)(ln reaharvestedaAb1,9117 1,8004 2,39 *** 0,3428 3,4805

)(ln creditCb-2,6287 0,6895 -3,81 *** -3,9801 -1,2771

)(lndefensivesDb0,0022 0,4079 0,01 -0,7974 0,8018


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)lim(ln estoneRb1,1503 0,7372 1,56 -0,2945 2,5952

))2/1(( AAAA bbb-0,3438 0,0810 -4,24 *** -0,5025 -0,1849

))2/1((CCCC

bbb0,1024 0,0583 1,76 ** -0,0118 0,2167

))2/1(( DDDD bbb-0,0006 0,0323 -0,39 -0,0759 0,0507

))2/1(( RRRR bbb-0,0658 0,0693 -0,95 -0,2017 0,0702

)( AAt tbb-0,0149 0,0231 -0,64 -0,0602 0,0304

)( CCt tbb-0,0193 0,0200 -0,97 -0,0585 0,0198

)( DDt tbb-0,0006 0,0097 -0,06 -0,0196 0,0185

)( RRt tbb0,0189 0,0193 0,98 -0,0190 0,0568

ACb0,1267 0,0577 2,19 *** 0,0134 0,2399

ADb0,0180 0,0425 0,42 -0,0652 0,1013

ARb0,1189 0,0516 3,66 *** 0,0879 0,2903

CDb-0,0029 0,0239 -0,12 -0,0498 0,0440

CRb-0,1518 0,0425 -3,56 *** -0,2352 -0,0682

DRb-0,0351 0,0413 -0,85 -0,1161 0,0458

1d (dummy North region)0,8565 0,1539 5,56 *** 0,5546 1,1582

2d (dummy Southeastregion)

1,0735 0,2525 4,25 *** 0,5785 1,5684

3d (dummy South region)

1,1111 0,2599 4,27 *** 0,6016 1,6206

4d (dummy Center-Westregion)

1,2213 0,1893 6,45 *** 0,8503 1,5923

0b15,1157 5,8720 2,57 *** 3,6067 26,6246

m 0,9707 0,6959 1,39 -0,3932 2,3346

h -0,1290 0,0395 -3,26 *** -0,2066 -0,0514

2ln s -1,7685 0,4409 -4,01 *** -2,6327 -0,9043

ilgtg 2,1697 0,5366 4,04 *** 1,1179 3,2215

2s

0,1705 0,0752 0,0718 0,4048

g 0,8974 0,0493 0,7536 0,9616


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2

us0,1530 0,0756 0,0048 0,3013

2

vs0,0174 0,0023 0,0129 0,0220


stchastic frntier mdel.Note: *** signicant to the 1% level; ** signicant to the 5% level; * signicant to the 10% level.

In Table 3 are presented the statistical tests applied in order to verify the consistency of specic hypothesisrelated t the prductin functin frntier adpted in the empirical mdel.

Tabe 3 lo likeiood Test of Stocastic Production Frontier Parameters

Test Null Hypothesis Value of l Prob>2

c

Decision

(5% level)

1 0......:0 ======= DRACRRAAttH bbbbb40.71 0.0000

Reject H0

243210 : dddd ===H

50.67 0.0000Reject H

0

30:

2

0 ====== RDCA ttttttH bbbb6.23 0.3984

Accept H0


stchastic frntier mdel.

The rst null hypothesis relates to the adequacy test

f Cbb-Duglas mdel relative t the less restric-

tive functinal frm expressed by the translg. Thus,

it is tested the hypthesis that all the secnd rder

coecients and the cross products are equal to zero.

The value of the log likelihood ratio, 40.71, is greater

than the critical value f the statistic ith

5% signicance level to the right.

Duy and Papageorgiou (2000) reject the Cobb-

Douglas specication utilizing a data panel for 82

countries in a period of 28 years. Additionally, by ex-

amining the impact f prductin technlgy ver

technical eciency, Kneller and Stevens (2003) reject

the specication of the aggregate production func-

tion over the eciency measures. Thus, translogproduction function constitutes a more exible rm

and is an apprximatin fr any prductin frntier.

The result f this test is presented n Table 2 rejects

the specication in the form of a Cobb-Douglas func-

tion in favor of the translog specied model.

The second analysis refers to the joint signicance tests

f the parameters f the variables that explain technical

ineciency. The result rejects the hypothesis that the

parameters are simultaneusly equal t zer.

The last test examines the stability f the prductinfrntier in relatin t the time variable, that cnsti-tutes the presence r nt f technlgy prgress inthe analyzed perid. Thus, the result f the test ac-

cepts the null hypthesis that there have nt beenany f the knn frms fr the sample and the ana-lyzed perid.

Accrding t the data f the analyzed perid, it isbserved that an ameliratin f aggregate prduc-tivity exists ver time. In a decreasing rder, the Bra-zilian regins that represent greater relative degreeof eciency were the Northeast, North, Southeast,Suth and Center-west regins. This result pintst the ne Brazilian agriculture frntiers herethe prductin f grain crps advances rapidly, fl-

led by livestck activity.

Additionally, the most signicant inputs that havecntributed t Brazilian agriculture prductivityere land factr, as ell as agriculture credit. on thether hand, the inputs related t agricultural defen-sives and limestone were not signicant to explainBrazilian agriculture prductivity thrughut theanalyzed perid.

According to the Economic Bulletin by IPEA (Brazil-ian Institute of Applied Economic Research), consid-


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ering the agriculture years 2000/2001 to 2004/2005,the sector has increased its debt in R$ 41,8 billionslely due t investment credit, cnstituting half fthe ttal agriculture credit. The investment creditdiers for not having annual cycle as credit destinedfr cvering csts destined t cver nrmal expenses

f prductin cycles. It is cumulative and exerts sig-nicant importance in the analysis of behavior in theagriculture sectr.

Fr illustratin purpses, cnsidering nly the agri-culture years 2003/2004 and 2004/2005, the sector hascntracted additional debt of R$20,9 billion, only oninvestment rubric - almst the same value f credit

for costs which was, on average, R$ 22 billion (B.

CONJ. IPEA, 2005). Thus, agriculture credit inserted

in the mdel is an adequate and relevant prxy fr

the representatin f machinery in the cntributin

f prductivity in Brazilian agriculture.

4.3 Data Envelopment Analysis (DEA): Malmquist

Index

Utilizing data frm LSPA/IBGE fr the main grain

crps in Brazilian agriculture rice, beans, maize,

sybeans and heat the flling results have

been btained accrding t Table 5.

Table 5 Total Factor Productivity Means and its Components, Grain Crops, Brazil (2001-2006)

Crp MalmquistIndex

Technical

change(TECH)

Eciency

change(EFCH)

Change

in PureEciency(PEC)

Change inScale (SEC)

Rice 1.152 1.270 0.907 0.930 0.975

Beans 1.303 1.270 1.027 1.013 1.013

Maize 1.300 1.270 1.024 1.020 1.004

Sy 1.262 1.270 0.994 0.970 1.024

wheat 1.218 1.270 0.959 1.001 0.958

Mean 1.246 1.270 0.981 0.986 0.995

Surce: Elabrated by the authrs.

In the perid frm 2001 t 2006, PTF in main Bra-

zilian grain crops increased 24.6% according to cal-

culatin f Malmquist indexes. The cmpnent f

this grth as the technical change index, hich

increased 27%. On the other hand, the component

referring to eciency change declined 1.9% during

the period. Thus, it is considered that the eect of

technlgy innvatin during the perid in study

has been more expressive than eect in eciency

change fr the analyzed crps.

Amng analyzed crps, beans ere the culture that

underwent the greatest increase in TFP (+0.30%)

during the observed period. In addition, it 5% is

analyzed that the principal cmpnent f such TFP

increase was technical change (+27), since growth in

eciency responded for only 2.7% of TFP elevation.

Decomposing the EFCH index, it is veried that the

indexes of pure eciency change and scale change

have responded for 50% of the underlying index in-

crease, given the 1.3% growth for both.

Maize culture as the crp that btained the sec-nd largest rise in TFP during the analyzed pe-riod. It is observed that its increase of 30% in theMalmquist index is predminantly due t technicalchange, which incurred an increase of 27%, simi-larly t glbal mean f data in study. Hever, thecomponent of technical eciency did not suer aregress, but a 2.4% increase. Among its subcom-pnents, the elevatin f the EFCH index ccurredmainly due to change in pure eciency, which pro-

gressed 2%, while the change in scale componentsuered a 0.4% increase.

It is also observed that the soybeans culture sueredthe third major increase in TFP (+26,2%), in whichindex f technical change as predminant verchange in eciency. However, in contrast to thesybeans culture, there has been a regress in changein eciency (-0.6%). It is veried that such declinein this cmpnent ccurs due t the regressin fchange in scale, which presented a 3% decline, andnt because f alteratins in the cmpnent refer-


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ring to scale change, which obtained a 2.4% growthduring the study perid.

Additionally, the wheat crop obtained the 4th majorelevation in TFP (+21.8) throughout the observed pe-riod, in which eects occurred exclusively by eectsin technical change, in hich technlgy innvatinis implicit, which in turn obtained a 27% progress,crrespnding t the mean f crps in study. H-ever, there has been eciency change for this culturethroughout the analyzed period (-4.1%). Among itscmpnents, the regressin in this item ccurreddue to changes in scale, which suered a decline of4.2% during the years from 2001 to 2006. In dierentcircumstances, an ameliratin r stability in this in-dex would have been veried, since the componentreferring to change in pure eciency for the wheatcrop obtained a 0.01% progress.

It is bserved that, amng main Brazilian graincrops, the rice culture suered the smallest growthin TFP between 2001 and 2006 (+15.2%). Similarly toother crops, a progress in technical change (+27%)is bserved. Hever, the regress in the index re-lated with change in eciency was the most expres-sive between the analyzed grains (-9.3%), being theunique culture to suer a decrease in pure eciency(-7%) and change in scale (2.5%).

Thus, all main Brazilian grain crps incurred in

prgress by the index referring t technical change.In ther rds, it is bserved the dislcatin f thetechnlgy frntier, nce detected that, n average,

the prduct f a crp at is greater thanthe ptential maximum prduct that culd have

been btained at in relatin f prductin fac-

trs f .

The component that negatively inuenced in theMalmquist index performance veried in the cul-tures f rice, sybeans and heat relates t change ineciency. Given that this component of change ineciency, calculated in relation to CRS technology,can be decomposed in changes in pure eciencyand changes in eciency, it is observed that allcrops experience regress either in pure eciencyonly change in eciency in relation to the VREfrntier, as is the case f sybeans - r slely the re-gress in scale change ratio between change in ef-ciency and change in pure eciency, representingalteratins in deviatins beteen technlgies CRSand VRE as ccurred ith the heat culture. H-ever, exception is veried for rice culture in which

both types of regress related to changes in eciencyccurred.

From Tables 6, 7 and 8, we verify the annual TFPevolution and its principal components eciencychange (approximation to the frontier) and techni-cal eciency (innovation) for each crop, analyzingchanges particularly amng the last studied perids(2005/2006).

Table 6 Total Factor Productivity, Grain Crops,Brazil (2001-2006)

Year Rice Beans Maize Soy Wheat

2002 0.719 1.113 1.327 1.310 1.297

2003 1.538 1.194 4.057 2.720 3.498

2004 2.407 1.802 0.644 1.235 0.987

2005 1.445 1.504 1.153 0.878 0.757

2006 0.526 1.045 0.929 0.830 0.790


Table 7 Eciency Change, Grain Crops, Brazil

(2001-2006)


2002 0.649 1.005 1.198 1.182 1.171

2003 0.414 0.321 1.091 0.731 0.941

2004 2.666 1.996 0.714 1.367 1.093

2005 1.397 1.454 1.115 0.849 0.732

2006 0.614 1.218 1.084 0.967 0.921


Table 8 Technical Change, Grain Crops, Brazil

(2001-2006)


2002 1.108 1.108 1.108 1.108 1.108

2003 3.719 3.719 3.719 3.719 3.719

2004 0.903 0.903 0.903 0.903 0.903

2005 1.034 1.034 1.034 1.034 1.034

2006 0.858 0.858 0.858 0.858 0.858


Frm the presented tables, it is bserved that nlythe culture f beans increased in its TFP frm 2005 t2006. We analyze that eciency changes surpassed


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the negative perfrmance f the cmpnent relatedd innvatin. on the ther hand, maize culture asthe sle crp besides beans that btained an increasein the component related to change in eciency.Hever, this prgress did nt cmpensate the de-cline suered by the technical change index.

Thus, taking into account the hypothesis that rmsmark-ups are psitively related t prductivity, thecrps f rice, heat, sy and beans incurred in thelargest declines in mark-up in 2006 - mainly due ttechnological issues but also signicantly aected by eciency. For the last two periods, the largestand nly mark-up increase is bserved fr beans.Following Sumanth (1985), since the productivityhas grown at a larger velocity (in this case, due to ef-ciency change) than other crops, mark-up increasefr beans has been favred due t ler csts that

are not entirely transmied to consumers.

A general decline in technlgical change certainlyaected mark-ups negatively for all grain crops inBrazilian agriculture. Therefre, the manner in hichfarmers culd maintain and increase their mark-upshas been either by exprts, since higher mark-upscan be charged due t the presence f trade csts,or increase in eciency that aects mark-ups to allmarkets. Assuming that cmmdity prducers areessentially price takers, ttal factr prductivity isthe ultimate frm f cst decrease and pprtunity

fr greater mark-ups bth dmestically and abrad.Hever, in 2006 in particular, technlgy has ntbeen able t functin as a tl fr cst decrease andmark-up increase in the agriculture f grain crpsin Brazil.

Cmmn evidence t all analyzed cultures is thedecline in technlgy cmpnent in 2006 as cn-sequence f agriculture crisis and its indebtednesswhich aected mainly grain crops, thus interferingin the acquisitin f inputs such as machinery andfertilizers that uld represent technlgy innva-

tin captured by this cmpnent in Malmquist in-dex fr increase in prductivity.

Accrding t IPEA, the increase in indebtednessoccurred because of two conditions satised: ex-cessively ptimistic expectatins in relatin t thefuture and a generus supply f credit given the un-derlying business risk. The ptimistic expectatinsere n the basis f increase in cmmdities pricesthat cincided ith exchange rate devaluatin, seenas a permanent phenmenn ith the end f anchrcurrency in 1999 and Chinese economic growth.

on the ther hand, the expansin f agriculturalfrntier especially in the Center-west fr the graincrps as cvered by credit frm private and pub-lic banking institutins, as ell as by prduct sup-plier rms. The crop expansion was associated witha high indebtedness f prducers in the shrt and

long term, inducing the nancial system to restrictindustrys access t ne brrings, interfering inmaintenance f the current level f activities and,therefore, reecting on acquisition of new technolo-gies for productivity increase (B. CONJ. IPEA., 2005,2006, 2006a, 2007).

Nnetheless, even ith gvernment interventin byrenegtiatin f farmers debts in 2006, accumulateddebts cntinue t sl a ne expansinary leap inactivity that would be veried by positive techno-lgical indexes, depressing the ptential capacity

fr grth and making ne investments unfeasiblebth fr the incrpratin f ne areas and fr capi-tal seeking prductivity increase. Thus, the nega-tive perfrmance in 2006 in technlgy change frall cultures is evidenced by dnfall in agricultureinputs usage such as fertilizers and limestone (B.CONJ. IPEA., 2005, 2006, 2006a, 2007).

5. CONClUSION

In this paper, the technique f Stchastic FrntierAnalysis has been applied fr the estimatin f in-

crease or decrease in ineciencies through time, asell as the linear prgramming methd Data Envel-pment Analysis and Malmquist index fr the anal-ysis f TFP surces fr the Brazilian crps f beans,maize, sybeans, heat and rice cnsidered themain grain crps in Brazil thrughut the peridthat cmprehends the years frm 2001 t 2006, themst recent data available.

Accrding t the Cbb Duglas mdel, e verify thatthe greatest elasticity bserved is that f harvestedarea, followed by credit variable, conrming the im-

prtance f agriculture credit t cver csts and, par-ticularly, t execute investments hich respnds frthe greatest share f the data analyzed. As expected,assuming psitive and inferir elasticity in relatint the ther relevant factrs, limestne cntributesfr prductivity by crrecting sle acidity, hich as-sumes a maximizing rle fr the ptential f prduc-tivity already established by the ther factrs.

In the stchastic frntier analysis fr the Brazil-ian agriculture, assuming a Translg technlgy, itis bserved n increase in aggregate prductivity


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thrughut the analyzed perid. In a decreasing r-der, the Brazilian regins presenting the highest rel-ative degree of eciency were the Northeast, North,Sutheast and Center-west. This results pints tthe ne Brazilian agricultural frntiers here graincrp prductin advances rapidly, flled by live-

stck activity.

Additionally, the most signicant inputs that contrib-uted fr Brazilian agriculture prductivity ere landfactor, as well as the agriculture credit the laer be-ing an adequate and relevant prxy fr representa-tin f machinery in the cntributin fr Brazilian ag-riculture prductivity. on the ther hand, the inputsrelated t agricultural defensives and limestne erenot signicant to explain Brazilian agriculture pro-ductivity thrughut the bserved perid.

on the ther hand, the Malmquist indexes revealedclarifying results fr independent crp analysis. Inrelatin t the means thrughut the study perid,it is bserved that majr TFP changes ccurred, in adecreasing rder, fr the cultures f beans, maize,sybeans, heat and rice. Althugh the mean varia-tins have indicated psitive TFP changes, hen an-alyzing changes beteen the years f 2005 and 2006,it is veried a decline in the component representingtechnlgy innvatins fr all majr Brazilian graincrops, jointly with the loss of productive eciencyfr all cultures, excepting beans and maize.

Thus, taking into account the hypothesis that frmsmark-ups are positive reated to productivit, tecrops of rice, weat, so and beans incurred in telargest declines in mark-up in 2006 - mainly due totechnological issues but also signifcantly aectedby eciency. Hever, nly the beans crp assumedpsitive variatin in its TFP, since it as the nly cul-ture amng principal Brazilian grain crps in hicheciency gain surpassed the negative eect of tech-nlgy use. The generalized decline in the technl-gy cmpnent can be explained by the indebted-ness crisis in agriculture that aected particularlygrain crps in 2005/2006, generating a dnfall inthe emplyment f agriculture inputs and interfer-ing negatively in the maintenance f current levelf agriculture activities in Brazil and, especially, asbserved fr the grain cultures analyzed.

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AUThORS BIOgRAPhy

Pauo Dutra Costantin received his B.S. in Economics from Universidade Federal de Uberlndia (1993) and com -pleted the Foreign Trade Specialization at Universidade Federal do Rio de Janeiro (1995). He received his mastersdegree in Economics from Fundao Getulio Vargas - SP (2000), and his PhD in Business Administration at Univer-sidade Presbiteriana Mackenzie (2007). Costantin is a full time Professor in Economics and Advisor for StrategicPlanning at Universidade Presbiteriana Mackenzie. His research focuses on Total Factor Productivity (TFP), VectorError Correction Model (VECM), Cobb-Douglas and Translog Production Function.

Dioenes Manoe leiva Martin received his B.S. in Business Administratin frm Funda Getuli Vargas - SP(1983), a B.S. in Economics from Universidade de So Paulo (1989), and a Bachelor of Law from Pontifcia Uni -versidade Catlica de So Paulo (1982). He received his masters degree (1989), and his PhD (1996) in BusinessAdministration from Fundao Getulio Vargas - SP (1996). Martin is a full time Professor in Economics and at thePostgraduate Program in Business Administration at Universidade Presbiteriana Mackenzie (PPGA/Mackenzie).His research fcuses n Investment Valuatin, Risk Management, Agribusiness, Finance Thery, and Applied Fi-nancial Ecnmetrics.

Edward Bernard Bastiaan Rivera Rivera received his B.S. in Business Administration (2006) and a B.S. in Econom-ics (2007) from Universidade Presbiteriana Mackenzie. In 2008, he joined the Postgraduate Program in BusinessAdministration at Universidade Presbiteriana Mackenzie (PPGA/Mackenzie) as a masters student in the Stra-tegic Finance research area, in hich he has been aarded a CAPES/PRoSUP Type I schlarship. Rivera Rive-ras research focuses on Cash Flow at Risk, TFP (DEA, Malmquist, Stochastic Frontier), Comparative Advantages(Balassa, Vollrath, Contribution to the Trade Balance), Resource Based View, Econometrics, Hedonic Prices, OpenMacrecnmics, Present Value Mdel, Unit Rt and Cintegratin.

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