Production efficiency in Indian agriculture: An assessment of the postgreen revolution years

Subhash C. Ray a,n, Arpita Ghose b

a University of Connecticut, Storrs, CT, USAb Jadavpur University, Calcutta, India

a r t i c l e i n f o

Article history:Received 27 January 2011Accepted 29 August 2013Available online 23 September 2013

Keywords:Data Envelopment AnalysisPareto-Koopmans EfficiencyModern and traditional inputs

a b s t r a c t

In this paper we use the nonparametric method of Data Envelopment Analysis (DEA) to obtain Pareto-Koopmans measures of technical efficiency of individual states over the years 1970–71 through 2000–01in a multi-output, multi-input model of agricultural production. We disaggregate overall efficiency intotwo distinct components representing output and input efficiencies and identify the contribution ofindividual outputs and inputs to the measured level of overall efficiency. Because introduction of moderninputs has been a major component of the process of modernization of Indian agriculture, we examine towhat extent different states succeeded in utilizing the modern inputs compared to the traditional inputs.Variations in the DEA efficiency scores across states and over years is explained in terms of differences invarious institutional and demographic factors in a second stage regression analysis.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Popularly known as the Green Revolution, the new agriculturalpolicy introduced in India in the late 1960s ushered in an era ofmodernization in the country's traditional agriculture that hadchanged little from the Colonial days over the first two decadessince Independence from British rule in 1947. The main pillars of theGreen Revolution were introduction of high yielding varieties (HYV)of wheat and rice, widespread use of chemical fertilizers, introduc-tion of agricultural machinery (like tractors and pump sets), extend-ing irrigation to a greater area under cultivation thereby allowingmultiple cropping, and creation of proper institutions for agriculturalcredit. Success of the Green Revolution is evident from the fact thatalthough deprivation and malnutrition remains an endemic problemin rural areas, India has achieved self-sufficiency in food and is nolonger dependent on imports or outright aid from donor countries tofeed its population. In a parallel manner, development of the non-food segment of the agricultural sector helps to foster growth oftextiles, food processing, and other agro-based manufacturing. Over-all, the extent of transformation of Indian agriculture over the firstthree decades following the Green Revolution is genuinely impress-ive. One cannot, however, ignore the fact that the index of food grainsproduction in 2002–03 fell by 18.6% from the level reached in theprevious year. This was preceded by a 6.66% drop in 2000–01 and

followed by a 7.04% drop in 2004–05. One suspects that the GreenRevolution is losing its momentum and another major breakthroughwould be needed to sustain the growth process. An importantobjective of this paper is to investigate whether greater productivityis achievable within the limits of the prevalent technology throughelimination of technical inefficiencies while Indian agriculture waitsfor the next major technological breakthrough.

There are numerous studies in the existing literature thatmeasure efficiency in Indian agriculture in the recent period. Mostof them used the econometric stochastic frontier analysis. Notableamong them are Kalirajan [17] who estimated a profit function forwinter rice, Kumbhakar and Bhattacharya [18] who estimateda generalized profit function incorporating price distortions result-ing from imperfect market conditions, socio-political and institu-tional constraints in jute cultivation, Bhattacharya and Kumbhakar[5] who estimated a generalized indirect production function alsofor jute, and Tadesse and Krishnamoorthy [27] who estimateda stochastic frontier production function for paddy. A notableexception is Sengupta [24,25] who applied three alternativeempirical approaches – stochastic frontier analysis, data envelop-ment analysis, and conventional regression analysis to analyze thesame data set from paddy cultivation.

Several of the studies (e.g., Shanmugam and Venkataramani [26])also have sought to explain the observed variation in technicalefficiency in terms of a number of farm characteristics like thefarmer's education and experience, contacts with agricultural exten-sion stations, access to credit, and farm size.

Two important points should be noted about the existingstudies. First, all of these studies are based on farm level data

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0305-0483/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.omega.2013.08.005

n Corresponding author. Tel.: þ1 860 486 3967; fax: þ1 860 486 4463.E-mail addresses: subhash.ray@uconn.edu (S.C. Ray),

aghosh@economics.jdvu.ac.in (A. Ghose).

Omega 44 (2014) 58–69

drawn from specific states (or regions within a state) and most ofthen consider the inputs and output of an individual crop over arelatively short period of time. As such, none of these studiesindividually nor all of them collectively can be regarded as a longterm analysis of production efficiency in agriculture at an All-Indialevel. Second, except for Sengupta [24,25] all of them use someexplicit parametric specification of the production (or cost) func-tion as the analytical format.

In this paper we use the nonparametric approach of DataEnvelopment Analysis (DEA) to obtain Pareto-Koopmans measuresof technical efficiency of individual states in India over the years1970–71 through 2000–01in a multi-output, multi-input model ofagricultural production. The Pareto-Koopmans efficiency measureis a complete measure in the sense that it reflects unrealizedpotential for increasing any output and decreasing any input thatthe firm has failed to exploit. Although there are some applicationsin other areas,1 to the best of our knowledge, this is the first studymeasuring Pareto-Koopmans efficiency in agricultural production.The main contributions of our paper can be highlighted as follows:

� Unlike the previous studies cited above, we examine the entireagricultural sector of the country rather than a sample ofindividual firms from a specific region. In that sense, ours isan analysis at the national level.

� We utilize a panel data set covering three decades following theGreen Revolution. This enables us to track how different regionsof the country have performed over this period. Becauseintroduction of modern inputs has been a major component ofthe process of modernization of Indian agriculture, we examineto what extent different states have succeeded in utilizing themodern inputs compared to the traditional inputs.

� In our empirical analysis, we disaggregate the overall efficiencymeasure into two distinct components representing output andinput efficiencies. Further, we are able to identify the contribu-tions of individual outputs and inputs to the measured level ofoverall efficiency. This permits us to focus separately on therate of utilization of the modern inputs like agriculturalmachinery, chemical fertilizers, and power.

� Use of a panel data set covering a long time period permits usto track how input efficiency, output efficiency, and overalltechnical efficiency has evolved over the years.

� We follow up the first stage DEA with a 2-way fixed effectspanel data regression in the second stage trying to explain theobserved variation in efficiency across different states and overthe years covered by this study.

The rest of the paper is organized as follows. Section 2 providesan overview of the nonparametric methodology. Section 3 describesthe data and reports the empirical findings from the efficiencyanalysis. A statistical analysis of the factors explaining the observedvariation in technical efficiency is presented in Section 4. The mainconclusions and policy implications are summarized in Section 5.

2. The nonparametric methodology

2.1. The technology and technical efficiency

Consider an industry producing bundles of m outputs y frombundles of n inputs x. The production technology is defined by the

production possibility set

T ¼ fðx; yÞ : y ARmþ can be produced from x ARn

þ g; ð1Þ

An input–output bundle (x0, y0) is feasible if (x0, y0)AT.The bundle (x0, y0) is weakly efficient in its input-orientation if it

is not possible to reduce all inputs simultaneously without redu-cing any output. That is,

ðx0; y0ÞAT and βo1 ) ðβx0; y0Þ=2T : ð2aÞSimilarly, (x0, y0) is weakly efficient in its output-orientation if

ðx0; y0ÞAT and α41 ) ðx0; αy0Þ=2T : ð2bÞThat is, all outputs cannot be increased simultaneously withoutincreasing any input.

Note that input-oriented weak efficiency does not precludereduction in one or more (though not all) inputs. Similarly, output-oriented weak efficiency is compatible with increase in one ormore individual outputs. Thus, weak efficiency does not implyPareto efficiency. Both input- and output-oriented weak efficien-cies are essentially radial in nature because one considers radialcontraction of the input bundle or a radial expansion of the outputbundle.

By contrast, (x0, y0) is strongly input-efficient only if a reductionin any component of the x0 input bundle would render the outputbundle y0 infeasible. That is

ðx0; y0ÞAT and xrx0 ) ðx; y0Þ=2T : ð3aÞIn an analogous manner, (x0, y0) is strongly output-efficient only if

ðx0; y0ÞAT and yZy0 ) ðx0; yÞ=2T : ð3bÞFinally,ðx0; y0ÞAT is Pareto-Koopmans efficient if both of thefollowing conditions simultaneously hold:

ðiÞ xrx0 ) ðx; y0Þ=2T ; ð4aÞand

ðiiÞ yZy0 ) ðx0; yÞ=2T : ð4bÞThus, strong input- and output-efficiency are both necessary andare together sufficient for Pareto-Koopmans efficiency.

Although useful for a summary evaluation of performance,the measured level of weak efficiency (whether input- or output-oriented) fails to provide a proper benchmark for improvement. Inorder to become fully efficient a firm has to eliminate underproduc-tion of every output and at the same time avoid underutilization ofevery input. Apart from providing a target input–output bundle thatthe firm should try to attain, Pareto-Koopmans analysis providesinput- and output-specific measures of efficiency.

2.2. Data envelopment analysis

In order to calibrate any of the various technical efficiencymeasures considered above, we need to construct the productionpossibility set empirically from observed data. In parametricmodels, one starts with an explicit specification of the productiontechnology in the form of a production function (in the singleoutput case) or a transformation function (in the multiple outputcase) and uses appropriate statistical methods to obtain estimatesof the parameters of the specified function from sample data.By contrast, in the nonparametric approach of Data EnvelopmentAnalysis (DEA) one makes a number of fairly general assumptionsabout the underlying technology but specifies no explicit func-tional form. Introduced by Charnes, Cooper, and Rhodes (CCR) [8]and further generalized by Banker, Charnes, and Cooper (BCC) [3],DEA allows one to construct the production possibility set empiri-cally from observed data. Specifically, one makes the following

1 Ray and Jeon [23] measured the Pareto-Koopmans efficiency of America'stop-rated MBA programs.

S.C. Ray, A. Ghose / Omega 44 (2014) 58–69 59

assumptions:

(i) Each input–output bundle (xj, y j) (j¼1,2,…,N) actuallyobserved in the sample is feasible.

(ii) The production possibility set T is convex.(iii) Inputs are strongly disposable. That is, if ðx0; y0ÞAT and x1Z x0,

then ðx1; y0ÞAT .(iv) Outputs are freely disposable. That is, if ðx0; y0ÞAT and y1ry0,

thenðx0; y1ÞAT .(v) If constant returns to scale hold, if ðx0; y0ÞAT , then ðkx0; ky0ÞAT

for all kZ0.

It can be easily verified that the free disposal convex hull of theobserved input–output data

SV ¼ ðx; yÞ : xZ ∑N

1λjx

j; yr ∑N

1λjy

j; ∑N

1λj ¼ 1; λjZ 0 ðj¼ 1;2; :::;NÞ

� �

ð5aÞis the smallest set satisfying assumptions (i)–(iv). The correspond-ing production possibility set satisfying the CRS assumption is

SC ¼ ðx; yÞ : xZ ∑N

1λjx j; yr ∑

N

1λjy j; λjZ0; ðj¼ 1;2; ::::;NÞ

� �ð5bÞ

2.3. Radial measures of technical efficiency

Following Banker et al. [3], the input-oriented radial technicalefficiency of a firm with an observed input–output bundle (x0, y0)under the variable returns to scale assumption is obtained as:

τxðx0; y0Þ ¼ min θ

s:t:∑N

1λjy jZ y0;

∑N

1λjx jrθ x0;

∑N

1λj ¼ 1;

λjZ 0 ðj¼ 1;2; :::;NÞ ð6ÞSimilarly, the output-oriented radial technical efficiency underVRS is measured as

τyðx0; y0Þ ¼ 1ϕn

where ϕn¼max ϕ

s:t:∑N

1λjy jZϕ y0;

∑N

1λjx jrx0;

∑N

1λj ¼ 1;

λjZ 0 ðj¼ 1;2; :::;NÞ ð7ÞWhen CRS is assumed, the restriction ∑N

1 λj ¼ 1 is deleted from (6)or (7). It is obvious that neither the input- nor the output-orientedradial measure of technical efficiency is affected by the presence(or magnitude) of slacks in any of the individual input or outputconstraints in (6) or (7).

2.4. Non-radial measures of technical efficiency

The problem of slacks in any optimal solution of a radial DEAmodel arises because we seek to expand all outputs or contract allinputs by the same proportion. In non-radial models, one allowsthe individual outputs to increase or the inputs to decrease at

different rates. Fare and Lovell [11] introduced the following input-oriented, non-radial measure of technical efficiency called theRussell measure:

ρxðx0; y0Þ ¼ min 1n∑

iθi

s:t:∑jλjyrjZyr0; ðr¼ 1;2…mÞ;

∑jλjxijrθixi0; θir1; ði¼ 1;2…nÞ;

∑jλj ¼ 1; λjZ0; ðj¼ 1;2;…;NÞ: ð8Þ

When input slacks do exist at the optimal solution of a radial DEAmodel, the non-radial Russell measure in (8) falls below theconventional measure obtained from an input-oriented BCC model(6). Because the radial projection is always a feasible solution for(8), ρxrτx: That is, the non-radial Russell measure of technicalefficiency never exceeds the corresponding radial measure.

The analogous output-oriented non-radial VRS measure oftechnical efficiency is:

RMyðx0; y0Þ ¼ 1=ρy;

where ρy ¼ max 1m∑

rϕr

s:t:∑jλjyrjZϕryr0; ϕrZ1; ðr¼ 1;2;…;mÞ;

∑jλjxijrxi0; ðI ¼ 1;2;…;nÞ;

∑jλj ¼ 1; λjZ0; ðj¼ 1;2;…;NÞ: ð9Þ

While no input slacks can exist at the optimal solution of (8),presence of any output slack is not ruled out. Similarly, inputslacks may remain at the optimal solution of (9). Thus, non-radialtechnical efficiency (whether input-oriented or output-oriented)by itself does not ensure over all Pareto efficiency.

It should be noted here that Charnes et al. [7] pointed out thatonce adjusted for the slacks in inputs and outputs, the radialefficient projection of an inefficient input–output bundle becomesPareto-Koopmans efficient. However, the slacks do not play anyrole in measurement of Pareto-Koopmans efficiency beyond thefact that unless all slacks are zero, any unit is not Pareto-Koopmans efficient even if its (radial) technical efficiency is foundto be equal to unity.

A non-radial Pareto-Koopmans measure of technical efficiencyof the input–output pair (x0, y0) can be computed as:

γðx0; y0Þ ¼ min1n∑

iθi

1m∑

rϕr

s:t: ∑N

j ¼ 1λjyrjZϕryr0; ϕrZ1; ðr¼ 1;2; :::;mÞ;

∑N

j ¼ 1λjxijrθixi0; θir1; ði¼ 1;2; :::;nÞ;

∑N

j ¼ 1λj ¼ 1; λjZ0; ðj¼ 1;2; :::;NÞ: ð10Þ

Note that the efficient input–output projection (xn, yn) satisfies

xn ¼ ∑N

j ¼ 1λnj x

jrx0 and yn ¼ ∑N

j ¼ 1λnj y

jZy0:

Thus, (x0, y0) is Pareto-Koopmans efficient, if and only if ϕrn ¼ 1 for

each output r and θin ¼ 1 for each input i, implying γðx0; y0Þ ¼ 1:

We can visualize the Pareto-Koopmans global efficiency measureas the product of two factors. The first is the input-orientedcomponent

γx ¼ 1n∑

iθi ð11aÞ

S.C. Ray, A. Ghose / Omega 44 (2014) 58–6960

and the second is an output-oriented component

γy ¼1

1m∑

rϕr

: ð11bÞ

Thus,

γðx0; y0Þ ¼ γx:γy: ð12ÞThis non-radial and non-oriented measure of technical efficiencywas introduced by Pastor et al. [19] as an Enhanced Russellmeasure and by Tone [28] as a Slack Based Measure (SBM) ofefficiency.2 A comparable multiplicative measure is the GeometricDistance Function introduced by Portela and Thanassoulis [21].

The objective function in (10) is non-linear. Both Pastor et al.[19] and Tone [28] transformed this linear fractional functionalprogramming problem into an LP problem by normalizing thedenominator to unity. Alternatively, as shown in Ray [22], one mayreplace the objective function by a linear approximation

γðx0; y0Þ ¼ f ðθ;ϕÞ

� f ðθ0;ϕ0Þþ∑iðθi�θ0i Þ

∂f∂θi

� �0þ∑

rðϕr�ϕ0

r Þ∂f∂ϕr

� �0

Note that

∂f∂θi

¼1n

1m∑

rϕr

and∂f∂ϕr

¼ �1n∑θi

1m ∑

rϕr

� �2:

Thus, using θ0i ¼ 1for all i and ϕ0r ¼ 1 for all r as the point of

approximation,

f ðθ;ϕÞ � 1þ1n∑

iθi� 1

m∑rϕr : ð13Þ

We may, therefore, replace the objective function in (10) by (13)and solve the linearized problem iteratively using the optimalsolution from each iteration as the point of approximation for thenext iteration until convergence

Once we obtain the optimal ðθn;ϕnÞ from this problem, weevaluate

γðx0; y0Þ ¼1n∑

i1m∑

rφr

: ð14Þ

as a measure of the Pareto-Koopmans efficiency of (x0, y0).Apart from an overall measure, (14) also provides information

about the potential for reducing individual inputs ðθni Þ and increasingindividual outputs ðϕn

r Þ: Also a decomposition of (14) into the input-and output-oriented components can be obtained from (12).

3. The empirical analysis

3.1. The data set

This study visualizes a two-output and seven-input productiontechnology for Indian agriculture.

The two outputs are: (a) food grains and (b) nonfood grains.The inputs included are:

(i) Land, (ii) Fertilizers; (iii) Irrigated Area; (iv) Pump sets;(v) Tractors, (vi) Electricity, and (vii) Labor. Further, the actualamount of rainfall is also treated as a non-discretionary input.

Seventeen major Indian States has been considered and areclassified into four regions:

(A) Eastern Region: Assam (AS), Bihar (BI), Orissa (OR), and WestBengal (WB);

(B) Northern Region: Haryana (HA), Himachal Pradesh (HP),Jammu and Kashmir (JK), Punjab (PU) and Uttar Pradesh (UP);

(C) Southern Region: Andhra Pradesh (AP), Karnataka (KA), Kerala(KE), and Tamil Nadu (TN);

(D) Western Region: Gujarat (GU), Madhya Pradesh (MP),Maharashtra (MH), and Rajasthan (RA).

Summary statistics for the input–output quantities and also theannual rainfall data are reported for All-India in Table 1. Compar-able statistics for the different regions are shown in Table 2. Inter-regional variation in the application of inputs per hectare is quiteapparent from Table 2. Relative to the states in the Eastern region,those in the Northern region use 2.15 as many pumps, 7.76 timesas many tractors, and 4.51 times as much power per hectare. TheSouthern states use over 7 times as much power, twice as manypumps, and nearly twice as much fertilizers as the Eastern states.The Western states use less fertilizers but more pumps, tractors,and power per hectare relative to the Eastern states. The percen-tage of gross cropped area irrigated is 39.4% in the Northern regionand only 18.73% in the Western region. Also, number of workersper acre is the lowest in the Northern region and the highest in theeastern region. Such difference in the input-mix may account forthe differences in the input utilization rates across the differentstates reported below in the empirical finding section.

3.2. The DEA findings

One problem faced at the outset was that with only 17 statelevel observations per year the DEA solution of an optimizationproblem involving 2 outputs and 7 inputs would not be verymeaningful. One way to address this ‘degrees of freedom problem’

is to carry out a window analysis by pooling observations frommultiple years for solving each DEA problem. In selecting thelength of a time window one needs to carefully balance theadvantages derived from an increase in the number of data pointsfor solving any DEA problem against the risk that the technologymay have changed within the time period covered by a largewindow. For the present paper, we selected a 2-year window.Overall and input- or output specific efficiencies for the initial andthe terminal year in our sample period were based on the optimalsolution of a single window. For intermediate years, optimalsolutions from consecutive windows were averaged to measurethese efficiencies.

Another limitation of the data is that the reported input–outputquantities were state level aggregates. We know that for anyindividual farm (j) in the state s the actual input–output combina-tion ðxsj ; ysj Þ is a feasible bundle. But what we observe for the stateis the aggregate bundle ðXs;YsÞ ¼ ð∑jxsj ; ∑jysj Þ: This aggregateinput–output bundle is feasible only if the underlying productiontechnology is additive, which implies constant returns to scale.We, therefore, assumed CRS in solving the DEA problems.

Estimated state-wise average levels of overall productive effi-ciency and its two principal components, input and outputefficiencies, are presented in Table 3. More detailed breakup ofthe input and output efficiencies are reported in Tables 4–6.

2 Although the (input or output) oriented radial model continues to be thepopular DEA model for measuring efficiency in most empirical applications, there isan increasing awareness of the importance of incorporating input and output slacksinto a comprehensive measure of overall efficiency. Asmild and Pastor [1] extendedthe multi-directional efficiency analysis (MEA) of Bogetoft and Hougaard [6] andthe Range Directional Model (RDM) of Portela, Thanassoulis, and Simpson [20] toobtain slack free comprehensive measures of efficiency. Edelstein and Paradi [10]introduced a multi-stage Proportional Slack Adjusted (PSA) methodology toincorporate Full Proportional Slacks (FPS) in a comprehensive efficiency measurethat is unit invariant.

S.C. Ray, A. Ghose / Omega 44 (2014) 58–69 61

3.3. Overall efficiency and its components

The all-India average level input technical efficiency (ITE) overthe entire sample period was 0.8543. That is, about 14.6% reduc-tion in the average level of inputs would be possible. Outputtechnical efficiency (OTE), averaged over all years and all states,was 0.7931 implying that on average output was about 79.3% of

the Pareto optimal level. The corresponding average level of ParetoKoopmans (PK) efficiency was 70.25%. At the regional level, theoverall input efficiency is highest in the Eastern region (0.914),followed by the Northern region (0.893). Western region (0.8289)and the Southern region (0.8026) performed much worse. Also,there was greater variation across states within the Southern andthe Western regions. By contrast, most states within the Easternregion and with the sole exception of one state, Jammu andKashmir (JK) in the Northern region showed quite high inputefficiency. In respect of output efficiency, while the Eastern region(88.6%) retained its rank at the top, the Southern region (85.65%)outperformed the Northern region (81.24%). The Western region(74.87%) came last. Most states with low output efficiency werefound to have low input efficiency as well. A glaring exception was

Table 1Summary statistics: All states and all years.

Variable Units Mean CV Min Max

Food metric tons (000) 9322.37 0.84 691.3 45238Nonfood metric tons (000) 16857.69 1.49 40 129294Frtl kilograms (000) 56.27 0.78 1.73 179.97Pump number (000) 617.58 1.47 2 8789Tract number (000) 666.79 1.67 3 6633Pwr kwh (millions) 2628.23 1.30 1.4 16218Lab persons (000) 10207.20 0.77 973 36174Irr hectares (000) 2638.49 0.92 91 12819Land hectares (000) 9186.84 0.71 840 26063Rain cm (per year) 1303.16 0.65 292.35 13062

Table 2Summary statistics: By region.

Variable Mean Std Dev Min Max

Region¼EasternFood 7794.25 3815.50 2115 15068Nonfood 8737.16 12955.09 1903 85713Frtl 36.89 35.13 1.73 133.77Pump 280.27 357.38 2 1199Tract 132.38 230.82 3 994Pwr 429.91 534.95 1.86 1771Lab 10285.66 6195.75 2945 25462Irr 1711.09 1009.56 433 3687Land 6965.49 2418.41 2872 11213Rain 1930.47 1184.88 899 13062

Region¼NorthernFood 11650.44 11529.70 890 45238Nonfood 19879.20 36723.06 40 129294Frtl 63.17 50.77 4.05 179.97Pump 760.79 1406.70 2 8789Tract 1293.97 1579.66 3 6633Pwr 2443.18 2710.57 1.4 9983Lab 7565.82 9909.94 973 36174Irr 3459.18 3536.45 91 12819Land 8766.88 8489.93 840 26063Rain 913.70 379.85 292.35 2138.6

Region¼SouthernFood 6887.10 3918.11 691.3 14535Nonfood 18382.73 12406.83 1358 53529Frtl 77.21 42.35 16.72 179.2Pump 626.24 396.27 32 1207Tract 278.43 271.43 13 1065Pwr 3309.82 3489.12 78.64 11748Lab 11115.27 5917.28 2804 23693Irr 2192.67 1333.61 226 4527Land 7606.61 3669.75 1301 12760Rain 1554.13 732.72 349 3213.9

Region¼WesternFood 9950.78 4934.30 2153 21016Nonfood 19608.67 18752.72 2215 75508Frtl 40.39 25.09 5.31 101.96Pump 769.38 324.30 139 1326Tract 642.78 699.75 70 2684Pwr 5020.63 4763.11 125.88 16218Lab 14174.59 5439.16 5711 22591Irr 2828.06 1322.10 1233 6741Land 15095.52 5041.37 6728 20388Rain 911.06 274.73 347 2096.9

Table 3Output, input, and overall efficiencies: (by Region and State).

Region/State OTE ITE PK

Eastern 0.8860 0.9140 0.8212AS 0.9812 0.9243 0.9106BI 0.7203 0.9139 0.6738OR 0.8469 0.8444 0.7301WB 0.9955 0.9735 0.9704

Northern 0.8124 0.8930 0.7603HA 0.9051 0.8881 0.8098HP 0.8295 0.887 0.7622JK 0.3701 0.7604 0.3291PU 0.9632 0.9503 0.9264UP 0.9943 0.9792 0.9741

Southern 0.8565 0.8026 0.7047AP 0.7155 0.8355 0.6114KA 0.9346 0.7288 0.6866KE 0.6528 0.6562 0.4432TN 0.992 0.9342 0.9282

Western 0.7487 0.8289 0.6393GU 0.6295 0.6866 0.4343MH 0.9659 0.904 0.8703MP 0.5422 0.9027 0.5185RA 0.4445 0.7621 0.3688

All-India 0.7931 0.8543 0.7025

Table 4Input efficiencies: Modern inputs.

Region/State Fertilizer Pump Tractor Power Modern

Eastern 0.8872 0.8884 0.9543 0.8418 0.8929AS 0.8526 0.8971 0.931 0.836 0.8792BI 0.9151 0.9297 0.9405 0.9625 0.9370OR 0.8298 0.7901 0.973 0.6037 0.7992WB 0.9514 0.9368 0.9726 0.965 0.9565

Northern 0.8536 0.9386 0.7799 0.7878 0.8400HA 0.8708 0.8671 0.7281 0.8389 0.8262HP 0.8065 0.952 0.7282 0.7718 0.8146JK 0.6798 0.9742 0.5958 0.4128 0.6657PU 0.935 0.9632 0.8782 0.9274 0.9260UP 0.9761 0.9367 0.9693 0.9881 0.9676

Southern 0.6427 0.7025 0.7387 0.5949 0.6915AP 0.6296 0.8513 0.9958 0.5981 0.7687KA 0.5896 0.676 0.4972 0.4783 0.5879KE 0.4334 0.3886 0.482 0.439 0.4985TN 0.9183 0.894 0.9799 0.864 0.9108

Western 0.9074 0.7067 0.7120 0.6069 0.7492GU 0.7563 0.3566 0.666 0.2474 0.4669MH 0.8936 0.9137 0.8398 0.8082 0.8784MP 0.9795 0.8707 0.7673 0.8061 0.8794RA 1 0.6859 0.5747 0.5659 0.7720

All-India 0.8220 0.8165 0.7948 0.7122 0.7864

S.C. Ray, A. Ghose / Omega 44 (2014) 58–6962

Madhya Pradesh (MP) in the Western region where outputefficiency was below 55% while input efficiency exceeded 90%.It may be noted that although average output technical efficiencyis lower than input efficiency across all states, at the individuallevel in 9 out of the 17 states output efficiency exceeded inputefficiency.

Tables 4 and 5 provide more details on the individual compo-nents of input technical efficiency. As noted at the beginning,introduction of modern inputs was an integral part of the newagricultural strategy in the Green Revolution era. In light of this,we divided the agricultural inputs into two broad categories:modern and traditional. Included in the modern category are:(i) fertilizers, (ii) pumps, (iii) tractors, and (iv) (electric) power.

The other inputs: (a) labor, (b) irrigation, and (c) land are treatedas traditional inputs. Use of chemical fertilizers, pumps for deepwell irrigation, tractors and tillers, and electric power are thehallmarks of the new technology. Of course, there is some measureof overlap in the sense that irrigation in the traditional categoryrelies on deep wells as the source and, hence, to a considerableextent, is closely related to pumps (and power).

For any individual input, the input-specific technical efficiencyof any particular state (reported in Tables 4 and 5) shows whatproportion of the actual quantity of that input used would berequired if the state operated at the selected Pareto-Koopmansefficient point on the frontier.

As can be seen from Table 4, at the All-India level, the averagelevel of input efficiency in respect of modern inputs was 0.7864implying a rate of under-utilization as high as 21.4%. Given thatthese non-traditional inputs account for a large part of the paidout costs in farming, this is quite disturbing. At the regional level,states in the Eastern region show high levels of input efficiency forall of the modern inputs. The Northern region also has performedfairly well. But the other two regions have performed ratherpoorly. In respect of individual inputs, inefficiency is mostpronounced in respect of power.

Low input specific efficiencies in respect of the modern inputscontrast sharply with much higher efficiencies in respect oftraditional inputs. As shown in Table 5, traditional input efficien-cies are uniformly high. The only exceptions were for Bihar (BI) inrespect of labor (71%), Jammu & Kashmir (JK) in respect ofirrigation (74%), and Rajasthan (RA) in respect of land (70.5%),

Table 6 shows a similar decomposition of the output efficiencyinto separate components for food grains and other (non-foodgrain) crops. For food grains, output efficiency is above 90% for allstates other than Kerala (KE), and Gujarat (GU). While a highaverage level of output efficiency in respect of food grains is goodnews, it also carries an implicit warning that there is not muchroom for increasing food supply by simply improving efficiencywithin the present technological frontier. Compared to food grains,efficiency in the production of other crops is much lower. It is clearthat lower output efficiency is driven mainly by low levels non-food efficiency in quite a few states. In view of the increasing levelof commercialization of agriculture in India, the poor performanceobserved in respect of the other crops is somewhat puzzling. It ispossible that because most of these products (like cotton and jutefiber) are produced as industrial raw materials, demand fluctua-tion in the relevant industries may restrict production well belowthe full potential. This, of course, is only a speculation that can beverified only with crop specific data. That is beyond the scope ofthe present study.

Table 5Input efficiencies: Traditional inputs.

Region/State Labor Irrigation Land Traditional

Eastern 0.9073 0.9376 0.9857 0.9385AS 1 0.9728 0.9864 0.966BI 0.7106 0.9606 0.9956 0.8889OR 0.9283 0.8515 0.9608 0.9135WB 0.9905 0.9657 1 0.9854

Northern 0.9692 0.9266 0.9896 0.9618HA 1 0.943 0.9667 0.9699HP 0.9638 1 0.9902 0.9847JK 0.8879 0.7405 1 0.8761PU 1 0.9571 0.991 0.9827UP 0.9945 0.9925 1 0.9957

Southern 0.8993 0.989 0.9872 0.9585AP 0.865 0.9941 0.9872 0.9488KA 0.9206 1 0.9824 0.9677KE 0.8823 0.9967 0.9792 0.9527TN 0.9292 0.9649 1 0.9647

Western 0.962 0.9597 0.8838 0.9351GU 0.9876 0.9493 0.8812 0.9394MH 0.936 1 0.9563 0.9641MP 0.9306 0.9917 0.9922 0.9715RA 0.9937 0.8979 0.7054 0.8656

All-India 0.9302 0.9528 0.9643 0.9491

Table 6Output efficiencies.

Region/State Food Non-food Output

Eastern 0.9957 0.8459 0.8860AS 1 0.9655 0.9812BI 1 0.6225 0.7203OR 0.9907 0.7954 0.8469WB 0.992 1 0.9955

Northern 0.9921 0.7804 0.7586HA 0.9606 0.8729 0.9051HP 1 0.7608 0.8295JK 1 0.3051 0.1007PU 1 0.9736 0.9632UP 0.9998 0.9895 0.9943

Southern 0.8946 0.8064 0.8238AP 0.9807 0.5935 0.7156KA 0.9041 0.9736 0.9346KE 0.7031 0.6637 0.6528TN 0.9903 0.9947 0.992

Western 0.9069 0.5266 0.7249GU 0.692 0.6086 0.6295MH 0.9442 0.9929 0.9659MP 0.9999 0.1719 0.5422RA 0.9915 0.3331 0.7621

All-India 0.95 0.7579 0.7931

Table 7Changes in efficiencies over time.

Sub-period 71-2/75-6

76-7/80-1

81-2/85-6

86-7/90-1

91-2/95-6

96-7/00-1

ITE 0.9447 0.9052 0.8206 0.8364 0.8553 0.7996Modern 0.9234 0.8725 0.7270 0.7504 0.7818 0.7323Fertilizer 0.9624 0.9076 0.7628 0.7729 0.7988 0.7836Pump 0.9057 0.8466 0.7411 0.7839 0.8052 0.8523Tractor 0.9359 0.846 0.736 0.7741 0.837 0.696Power 0.8897 0.8897 0.6682 0.6707 0.6862 0.5971Traditional 0.9730 0.9678 0.9452 0.9509 0.9532 0.8895Labor 0.9764 0.9595 0.9034 0.9045 0.9226 0.8535Irrigation 0.9762 0.9777 0.9729 0.9715 0.9579 0.8818Land 0.9665 0.9662 0.9594 0.9769 0.9793 0.9332OTE 0.9235 0.8812 0.7919 0.7662 0.7976 0.6505Food 0.9798 0.9866 0.9703 0.9424 0.9393 0.8931Non-food 0.9089 0.8429 0.7379 0.7203 0.7755 0.6225PK 0.8914 0.8132 0.668 0.6613 0.7147 0.542

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Another question that we address in this study is whether thereis any clear pattern in how input or output specific efficiency levelshave changed over time. The findings in this respect are reported inTable 7. To eliminate the effect of a random noise often found inyear-to-year variations, we focus on average levels of efficiency over5-year periods. In the first half of the 1970s, both input and outputefficiencies were quite high. Notably, the rate of utilization ofmodern inputs exceeded 91%. On the output side, both food grainsand other crops showed high efficiency. One may argue that theGreen Revolution got off to a good start. During the latter half ofthe 70s, even though efficiency with respect to modern inputs onthe one hand and non-food crop output on the other showed aslight decline, overall input and output efficiencies both remainedabove 90%. The next decade saw a drastic drop in efficiency withrespect to modern inputs as well as non-food output. Both of themwere between 72% and 74%. Particularly low were the utilizationrates of fertilizer and power inputs. During the first half of the1990s, there was some improvement in respect of moderninputs overall but efficiency in the utilization of power remainedbelow 70%. Over the last half of the 1990s, things worsened. Quitelow efficiency is found for tractors and power. For the first time,output efficiency fell below 90% for food grains. All in all, there is adecline in input and output efficiencies over time. This is particu-larly noticeable for non-food crops and for some modern inputs(especially, fertilizers and power).

4. Explaining the variation in input-, output-, andPareto-Koopmans efficiencies

4.1. The second stage regressions

The efficiency scores reported in Tables 3–6 provide a produc-tive performance audit for the individual states over the years andhelp to identify the better and the worse performing states. As isevident, there is considerable variation in efficiency across thestates. Such inter-state variation in the DEA measure of efficiencycan be partially explained by differences in the physical, social, andinstitutional environment within which a state operates. A second-stage regression analysis of the measured efficiency level can helpto identify factors that enhance or hinder efficient resourceutilization. This, in its turn, becomes helpful for public policy forimproving efficiency. We identify below a number of importantfactors and discuss their relevance as determinants of efficiency inagricultural production in a state in India.

4.2. Soil types

For agricultural production the importance of soil character-istics can hardly be overstated. There is a great diversity in soiltypes in the different regions of India. While the Indo-Gangeticplains and the Brahmaputra River valley in the Northern, North-Western, and North-Eastern parts of the country are rich in fertilealluvial soil. Large parts of Rajasthan and Northern Gujarat consistof sand dunes and sandy plains poorly suited for agriculture. Thesouthern part of the country is characterized by black soil. In orderto capture the influence of geological differences across regions,we include three dummy variables, NORTH, SOUTH, and WEST, forindividual states in the respective regions. By default, states in theEastern region belong to the base group.

4.3. Rainfall and type of irrigation

Adequate availability of water is an essential requirement for agood harvest. There is considerable variation in rainfall acrossdifferent parts of the country. While the impact of such climatic

difference would also be captured by the region dummy variables,a more precise measure of the effect of rainfall can be obtained byusing the state specific amount of annual rainfall (RAIN).

In the post-Green Revolution era, the newly introduced highyielding variety seeds and chemicial fertilizers have greatly enhancedthe importance of assured supply of water through deep well andcanal irrigation. Because private irrigation is relatively more expen-sive, for the same acreage of irrigated area a higher share of the areairrigated from government canals (GSHARE) makes it possible to useadequate amount of water for the modern variety crops. This wouldenhance input effieincy. On the other hand, a farrmer with access toprivately owned wells has a greater control on the irrigation input andhas more flexibility in the choice of crops. This would raise outputefficiency. By implication, GSHARE would lower output efficiencyceteris paribus.

4.4. High yielding variety crops

The Green Revolution was virtually embodied in the introduc-tion of the high yielding varieties of wheat and rice withsubstantially higher yield per acre than the traditional varieties.The proportion of the cutivated area under high yielding varietycrops (HYV) is expected to have a positive impact on efficiency.However, an overwhelmingly important factor in this respect isthe amount of rainfall and the marginal effect of HYV woulddepend on the amount of rainfall (RAIN). This can be accommo-dated by including interaction terms between HYV and RAIN.

4.5. Institutional and demographic factors

Modernization of traditional agriculture involves numerousstructural changes at different levels. The most important of themis replacement of age old farming parctices by a more advancedand knowledge based technology. Also important are other con-comittant changes like commericialization of a predominantlysubsistence agriculture through integration of an isolated villagebased economy into a national and eventual global economy andbreaking up rural monopolies in land though a more eaglatariandistribution.

Government expenditure on agricultural education, research,and extension (EDUR) contributes to human capital formation andfacilitates transtion from traditional to modern technology. Eventhe spread of basic education (raising the rural literacy rate) (RLIT)contributes towards increase in human capital. Because of thegrowing importance of purcahsed inputs, easy and timely avail-ability of agricultural credit (LOAN) would play a role in increasingefficiency.

It is well known that trade liberalization provides manybenefits such as increase in market size, knowledge of demandcharacteristics in foreign markets, information about new tech-nologies, processes, and products, cost reduction, and qualityimprovements. To what extent a state benefits from trade liberal-ization will depend on its share in the total exports of agriculturalproducts by the country as a whole. We use a measure of thedegree of openness (OPEN) of the state in respect of agriculturalproducts (explained in the Appendix) and include this as anexplanatory variable.

At the individual producer level, crop diversification makes thefarmer more competitive allowing it to access the market for agreater number of products. At the same time, excessive diversi-fication with the total area remaining unchanged means that lessand less acreage would be allocated to individual crops sacrificingpotential economies of scale. One may, therefore, expect a non-linear (quadratic) relationship between crop diversification (CD)and efficiency.

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Finally, land reforms reducing concentration of ownership is arecognized engine of productivity and efficiency growth in agri-culture. There are several individual country studies that foundevidence of a positive impact of lower inequality of land owner-ship on agricultural productivity.3 We include the Gini ratio (GINI)of the distribution of land ownership to capture the effects ofconcentration on productive efficiency.

4.6. Time dummy variables

The DEA (input-, output-, and Pareto-Koopmans) efficiencymeasures have all shown a general decline over years. This is alsoevident from the 5-year averages for the individual inputs andoutputs shown in Table 7. It is important to examine whether thisdownward movement can be attributed solely to adverse move-ment in factors affecting efficiency. We include year-specificdummy variables to identify the pattern of inter-temporal declinein efficiency not related to the explanatory variables.4

4.7. The regression results

We estimated three separate regressions with input efficiency(INP), output efficiency (OUT), and Pareto-Koopmans efficiency(PK), as the dependent variables. Explanatory variables5 includedwere (1) the Gini ratio of land distribution (GINI), (2) degree ofopenness (OPEN), (3) government spending on agricultural educa-tion and research (EDUR), (4) availability of agricultural credit(LOAN), (5) crop diversification index (CD), (6) rural literacy rate(RLIT), (7) the percentage of the gross cropped area under highyielding varieties of crops (HYV), (8) the proportion of irrigatedarea served by government canals (GSHARE), and (9) the amountof annual rainfall (RAIN) apart from the dummy variables for theregions (NORTH, SOUTH, and WEST) and years (T7475 throughT9899). By default, the common intercept refers to the Easternregion and the year 1973–74. The specified regression modelswere non-linear in some of the variables including several quad-ratic and interaction terms. This allows the marginal effects ofchanges in the regressors to vary across data points. Each regres-sion model was estimated by a two-way fixed effects panel dataregression adjusted for contemporaneous correlation (acrossunits) and cross section heteroscedasticity within a seeminglyunrelated regression (SUR) framework. Standard errors of esti-mated coefficients were obtained from a robust covariance matrix.Due to unavailability of some of the explanatory variables forselected years for individual states, we had to use an unbalancedpanel. The estimated regression coefficients along with the stan-dard errors are reported in Tables 8–10.

It may be noted that for all the three regressions (Input, Output,and PK Efficiency), coefficients of all of the time dummies arenegative and statistically significant. Moreover, the coefficients ofdummy variables for the later years are (with few exceptions)increasingly more negative. This confirms that there has been anautonomous decline in efficiency over the years. Also, the coeffi-cients of the region dummies (NORTH, SOUTH, and WEST) are allnegative and statistically significant implying that Eastern regionhas an efficiency advantage (possibly due to a superior soilquality). As for the other explanatory variables, not all of themwere found to be significant in each of the regressions. Moreover,the patterns of interaction and/or non-linearities also varied acrossregressions.

4.8. Input efficiency

In the regression for input efficiency (INP) shown in Table 8, themarginal effects of both EDUR and GSHARE are positive andconstant. On the other hand, while HYV, RAIN, OPEN, and CD havesignificant impact on input efficiency, their marginal effects varyacross data points. These variable partial effects (and their magni-tudes at the sample means of the variables concerned) are shownin Table 11. The partial effect of an increase in HYV on inputefficiency initially declines but subsequently increases with CD.The partial effect of an increase in CD declines with an increase ineither HYV or CD. But this is offset to some extent by an interactionbetween the two. The partial effect of RAIN is positive but declineswith an increase in RAIN. Similarly, input efficiency initiallyincreases with OPEN but this positive marginal effect gets atte-nuated as OPEN increase. At the sample mean of the data thepartial effects are 0.1317 for HYV, �0.1460 for RAIN, 0.0587 for CD,and 0.0184 for OPEN. The negative marginal effect of RAIN isconsistent with the fact that while adequate rainfall is essential foragricultural production, excessive rain can cause flooding andtransportation problems at which point the marginal effectbecomes negative. Judging by the expression for the relevantpartial effect shown in Table 11, the critical value for RAIN is0.1000 which is exceeded by the sample mean (0.1335).

4.9. Output efficiency

In the regression for output efficiency (OUT) shown in Table 9,three variables, EDUR, GSHARE, and GINI, have constant marginaleffects. Of these EDUR positively influences output efficiency whileGSHARE and GINI have negative effects. An increase in govern-ment expenditure on agricultural education and research (EDUR)provides farmers with easier access to information and guidanceabout the modern farming methods and would, naturally, have abeneficial effect on output efficiency. The negative coefficient ofGSHARE is in contrast with its positive effect on input efficiency.It should be remembered, however, that an increase in the share ofacreage irrigated from government canals implies a lower use ofprivate irrigation sources. As pointed out above, a farmer withaccess to private irrigation sources has more flexibility in the choiceof crops (like the winter Rice that is grown in the months of theyear when government canals have lower water levels). This mayexplain the negative effect of an increase in GSHARE (implying adecline in the share of private sources).

The negative coefficient of the GINI ratio in the regression foroutput efficiency is as anticipated and is consistent with a evidencefrom the existing literature. The negative coefficient in this regres-sion implies a detrimental impact of increased inequality in landdistribution on output efficiency. Share tenancy and cultivation bylandless farm workers accounts for a signification part of Indianagriculture. Due to well known incentive problems the share tenantrefrains from making long term improvements on land. This lowersoutput efficiency.

Three other variables, HYV, RAIN, and CD, also have significantimpact on output efficiency. But their respective marginal effects(shown in Table 12) vary across observations. For HYV, the marginaleffect depends on both the share of HYV in total cultivated area andthe level of rainfall. However, at the sample mean of the data thepartial effect of an increase in HYV on output efficiency is positive(0.0322). Similar nonlinearity is found in the marginal effect ofrainfall as well. Here also, the partial effect at the mean is positive(0.0536). The marginal effect of CD shows that output efficiencyinitially increases with crop diversification but beyond a pointfurther increase in CD lowers efficiency. At the sample mean thepartial effect is negative. Again, this over diversification may reflectuneconomically small scale of production for individual crops.

3 See, for example, Besley and Burgess [4], Jeon and Kim [16], Banerjee and Iyer[2], Deininger and Squire [9].

4 Rather than including a linear or quadratic time trend, we use year wisedummies so that year-to-year movements can be downwards as well as upwards.

5 For data definitions see the Appendix.

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4.10. Pareto Koopmans efficiency

In the regression for Pareto Koopmans efficiency (PK), threevariables, EDUR, RLIT, and GINI have constant marginal effects.Three other variables, HYV, RAIN, and CD, appear in non-linear andinteractive forms and have varying marginal effects. Each of the firstthree of these makes an interesting point. Education and research(EDUR) was significant with a positive coefficient in the regressionsfor both input and the output efficiency. It comes out as significantwith a positive coefficient in the regression for Pareto Koopmansefficiency as well. Rural literacy rate (RLIT) was not found statisti-cally significant for either input or output efficiency. Yet, it shows up

with a highly significant positive coefficient (with a ‘t’ ratio close to3.85) in the regression for Pareto Koopmans efficiency. Rural literacydoes not have a strong enough impact on either input or outputefficiency considered individually. But when the two factors arecombined into the overall Pareto Koopmans efficiency, the signifi-cant impact of this variable can be detected. Inequality in landownership (GINI) was found to be a significant factor for outputefficiency but not for input efficiency. However, the negative signand also the statistical significance of the coefficient persist even inthe regression for Pareto Koopmans efficiency. Yet another variable(GSHARE) makes an interesting point by its absence from thisregression. Recall that GSHARE was found to have a significant

Table 8Regression of input efficiency.

Variable Coefficient Std. Error t-Statistic Variable Coefficient Std. Error t-Statistic

C 0.328 0.194 1.69 T8384 �0.16527 0.003733 �44.2756HYV 1.33722 0.142608 9.376913 T8485 �0.1428 0.004071 �35.0728EDUR 0.002261 0.000207 10.93172 T8586 �0.15748 0.004584 �34.351GSHARE 0.057345 0.030715 1.867 T8687 �0.11158 0.003699 �30.1623CD 1.062426 0.025585 41.52496 T8788 �0.13394 0.003922 �34.151OPEN 0.020875 0.005032 4.148018 T8889 �0.1144 0.0043 �26.607RAIN 0.46355 0.178303 2.599786 T8990 �0.10461 0.004987 �20.9782(RAIN)2 �2.31772 0.572999 �4.04489 T9091 �0.07002 0.005641 �12.4115(CD)2 �0.26759 0.009469 �28.2598 T9192 �0.12272 0.005631 �21.7951(OPEN)2 �0.00072 0.000244 �2.95238 T9293 �0.16337 0.005323 �30.6879(HYV)(CD) �1.272 0.138406 �9.19036 T9394 �0.1919 0.014155 �13.5571(HYV)(CD)2 0.336852 0.038857 8.669087 T9495 �0.24907 0.021321 �11.6822T7475 �0.02473 0.002484 �9.95696 T9596 �0.2899 0.024579 �11.7948T7576 �0.03337 0.001375 �24.2648 T9697 �0.26474 0.020332 �13.0208T7677 �0.0527 0.001684 �31.2876 T9798 �0.3217 0.01928 �16.6854T7778 �0.02876 0.001451 �19.8281 T9899 �0.26632 0.017484 �15.2324T7879 �0.04632 0.002245 �20.6291 NORTH �0.04622 0.011879 �3.89089T7980 �0.12651 0.001992 �63.5115 SOUTH �0.1425 0.017238 �8.26685T8081 �0.13849 0.002198 �63.0079 WEST �0.09895 0.010407 �9.50814T8182 �0.12261 0.002567 �47.764T8283 �0.14829 0.002741 �54.0953

Dependent Variable: INP Method: Panel EGLS.Sample: 1974–1999; Periods Included; 26 Cross Sections: 17.Total (unbalanced) Panel Observations: 416.White-corrected Standard Errors.

Table 9Regression of Output Efficiency.

Variable Coefficient Std. Error t-Statistic Variable Coefficient Std. Error t-Statistic

C 0.80918 0.116186 6.964518 T8384 �0.29869 0.006657 �44.87HYV 0.296135 0.048275 6.134368 T8485 �0.30091 0.007794 �38.6082EDUR 0.005431 0.000343 15.8274 T8586 �0.28945 0.00821 �35.2542GSHARE �0.1741 0.035612 �4.88873 T8687 �0.2389 0.005796 �41.22CD 0.524861 0.113173 4.637684 T8788 �0.32835 0.007071 �46.4354GINI �0.22697 0.024103 �9.4169 T8889 �0.25312 0.007995 �31.6594RAIN 0.729503 0.145293 5.020915 T8990 �0.27335 0.009359 �29.2087LOAN 0.00267 0.000753 3.547625 T9091 �0.19772 0.010592 �18.6661(RAIN)(HYV) �2.60635 0.389381 �6.69355 T9192 �0.24275 0.010801 �22.475(CD)2 �0.16785 0.032157 �5.2197 T9293 �0.29921 0.010849 �27.5788(HYV)(RAIN)2 5.439961 0.840014 6.476038 T9394 �0.30212 0.011883 �25.4251(RAIN)(HYV)2 �0.10182 0.017801 �5.71989 T9495 �0.32741 0.01283 �25.5192T7475 �0.07439 0.002815 �26.4296 T9596 �0.40166 0.013427 �29.915T7576 �0.08928 0.001362 �65.5765 T9697 �0.46449 0.013873 �33.4802T7677 �0.15681 0.003375 �46.4627 T9798 �0.45851 0.015964 �28.7214T7778 �0.0782 0.002969 �26.3375 T9899 �0.50418 0.018336 �27.4969T7879 �0.0702 0.002779 �25.2639 NORTH �0.11745 0.023602 �4.97608T7980 �0.17846 0.002913 �61.2712 SOUTH �0.08205 0.018904 �4.34038T8081 �0.17576 0.00368 �47.7665 WEST �0.22588 0.027662 �8.16576T8182 �0.14833 0.003885 �38.1815T8283 �0.21436 0.005065 �42.3204

Dependent Variable: OUT Method: Panel EGLS.Sample: 1974–1999; Periods Included; 26 Cross Sections: 17.Total (unbalanced) Panel Observations: 416.White-corrected Standard Errors.

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impact on both input and output efficiency. However, the coeffi-cients were of opposite signs. This variable enhanced input effi-ciency but lowered output efficiency. In the regression for ParetoKoopmans efficiency, these opposing effects worked against eachother. As a result, GSHARE was not found significant.

4.11. Summary of findings

We may now summarize the main findings from the empiricalanalysis:

� There is clear evidence of an overall decline in both input- andoutput efficiencies over time. A broad downward trend in thedifferent DEA efficiency measures was revealed by the 5-yearaverages across subsequent sub-periods. Coefficients of thetime dummies in the second stage regressions confirmed thateven after one took explicit account of the various environ-mental factors, there was a secular decline in efficiency overthe years.

� Although the use of fertilizers, agricultural machinery, and powerhas increased phenomenally over years, rates of productiveutilization of the inputs has fallen. Moreover, there is considerablevariation across regions (and states within regions). Because useof these modern inputs is an integral part of the moderntechnology, potential benefits of the technological change remainunrealized to a large extent.

� There is little room for increasing food production simplythrough improved efficiency. Relatively high rates of utilizationof traditional inputs (especially land and irrigation) suggestthat these are the inputs that could limit increasing outputwithout another technological breakthrough.

� There is considerable inter-regional variation in the levels ofinput- and output-specific efficiencies. This is particularly truefor modern inputs and non-food output. Even within anyregion, there is considerable variation across states. Apartfrom agro-climatic factors there may be differences in thestate of development of physical infrastructures that accountfor such variation in efficiency.

4.12. Policy implications

Discussion of the fitted regressions has shown that not allvariables appear significant in all regressions. It should be recognized,

Table 10Regression of Pareto-Koopmans efficiency.

Variable Coefficient Std. Error t-Statistic Variable Coefficient Std. Error t-Statistic

C 0.341689 0.196065 1.742735 T8384 �0.39753 0.007383 �53.8418HYV 0.550066 0.050045 10.99132 T8485 �0.36638 0.008684 �42.1927EDUR 0.005987 0.000393 15.22125 T8586 �0.3725 0.009337 �39.8964CD 0.720503 0.185907 3.875617 T8687 �0.30391 0.007309 �41.5813RLIT 0.000969 0.000252 3.844991 T8788 �0.38685 0.007822 �49.4579GINI �0.03964 0.019449 �2.03808 T8889 �0.30633 0.0085 �36.0409RAIN 1.934348 0.610869 3.166553 T8990 �0.31791 0.009912 �32.0737(RAIN)2 �2.54653 0.572618 �4.44717 T9091 �0.22068 0.011178 �19.7417(CD)2 �0.21784 0.050852 �4.28375 T9192 �0.2947 0.011373 �25.9117(RAIN)(HYV) �2.06992 0.16566 �12.495 T9293 �0.36891 0.011473 �32.1534(HYV)(RAIN)2 0.17518 0.019706 8.889576 T9394 �0.36227 0.012349 �29.3369(RAIN)(HYV)2 0.081969 0.016881 4.855768 T9495 �0.3831 0.012782 �29.9716T7475 �0.08416 0.007374 �11.4136 T9596 �0.45715 0.014007 �32.6367T7576 �0.10317 0.001868 �55.2263 T9697 �0.52037 0.015177 �34.286T7677 �0.18607 0.003833 �48.5394 T9798 �0.5647 0.016223 �34.8097T7778 �0.10235 0.00296 �34.5729 T9899 �0.58668 0.017579 �33.3742T7879 �0.09982 0.004038 �24.723 NORTH �0.14116 0.023804 �5.93004T7980 �0.26858 0.003431 �78.278 SOUTH �0.18499 0.024802 �7.45865T8081 �0.27889 0.004184 �66.6525 WEST �0.21885 0.032606 �6.71187T8182 �0.23765 0.004162 �57.0937T8283 �0.31448 0.005553 �56.6369

Dependent Variable: PK Method: Panel EGLS.Sample: 1974–1999; Periods Included; 26 Cross Sections: 17.Total (unbalanced) Panel Observations: 416.White-corrected Standard Errors.

Table 11Marginal effects of selected regressors on input efficiency.

Marginal effects Partial effect atsample mean

∂INP∂HYV

¼ 1:3372�1:272CDþ0:3369ðCDÞ2 0.1371

∂INP∂RAIN

¼ 0:46355�4:6354RAIN�0.14601

∂INP∂CD

¼ 1:0624�0:5351CD�1:272HYVþ0:6737ðHYVÞðCDÞ 005878

∂INP∂OPEN

¼ 0:02088�0:00144OPEN0.01838

Table 12Marginal effects of selected regressors on output efficiency.

Marginal effects Partial effect at samplemean

∂OUT∂HYV

¼ 0:2961�2;60635RAINþ5:43996ðRAINÞ2�0:20364ðRAINÞðHYVÞ

0.03217

∂OUT∂RAIN

¼ 0:72950�2:60635HYV

þ10:87992ðHYVÞðRAINÞ�0:10182ðHYVÞ20.05356

∂OUT∂CD

¼ 0:52486�0:33570CD�0.09373

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however, that a factor that enhances either input or output efficiencycontributes, by definition, to an improvement in overall productiveefficiency (even though the impact may not appear statisticallysignificant in the regression for Pareto Koopmans efficiency). In lightof this, the regression findings have a number of policy implicationsfor improving efficiency. The important ones are summarized below.

� The significantly positive effect of EDUR in all of the threeregressions implies that government should increase expendi-ture on agricultural education and research.

� Given the positive effects of export orientation (OPEN) on inputefficiency, the government should actively seek to promoteexport of agricultural products.

� Based on the negative coefficients of GINI in both the output andPareto Koopmans efficiency, the government should carry outland reform in order to lower the inequality in land ownership.Apart from the social welfare effects of a more equal distributionof income, such land reform would also promote efficiency.

� Policies to raise the literacy rate among the rural population(RLIT) will increase overall efficiency.

� Limited crop diversification (CD) should be encouraged throughagricultural extension programs. However, that over diversifi-cation might result in too little land allocated to individualcrops because that could leave potential economies of scaleunexploited.

� Because of its positive impact on output efficiency, greateravailability of agricultural credit (LOAN) (often achieved throughIndia's public sector banks) should be an important component ofpublic policy.

4.13. A caveat

It is advisable to recognize, at this point, some limitations of thedata used and to acknowledge that the results should interpretedwith some caution. In the first place, we are using highlyaggregated data. Not only are the input–output data aggregatesover all farms in a state, they are also aggregated over crops and,hence, across different varieties of any crop (like traditional andhigh yielding varieties of rice or wheat). Similarly, inputs (likefertilizers) are also aggregated. Despite this limitation, our2-output multi-input framework is more disaggregated than whatis found in the relevant literature.

Another important point to remember is that state level effi-ciency measures computed for each year are based on the input–output data for that particular year only. In the jargon of DataEnvelopment Analysis, these are efficiencies relative to a contem-poraneous frontier. No attempt is made to measure efficiency against“cross-period frontiers”. This circumvents the question of technicalprogress. Standard Malmquist productivity analysis is based onradial DEA models and ignores slacks. A logical extension of thepresent study would be to measure productivity change over timeusing the Geometric Distance Function. That remains a futuredirection for research. In spite of these limitations, evidence ofthe downward movement in overall efficiency as well as in outputand input efficiencies is quite convincing.

5. Conclusion

It is well known from the general theory of diffusion of both ideasand products that there are four distinct stages in the process. Thenew idea is first embraced by innovators, the small percentage ofthe relevant population who dare to try something new. Then comethe early adopters, the more careful segment who prefer to wait-and-see first. Next are the late adopters, who are mainly driven by the

example of others. Finally enter the laggards. In the case of the GreenRevolution, it is reasonable to argue that the more productivefarmers with greater human capital came first. Over time, the lessproductive ones followed. This is a reasonable explanation of thedecline in efficiency (especially for modern inputs and cash crops)over time. In any event, it seems to be the case that Indian agricultureis likely to remain stagnant unless a new breakthrough in thetechnology takes place.

Appendix A

Data construction was carried out as follows:

� The Gini ratio of land distribution was constructed from theCensus of agriculture.

� Degree of openness was constructed in the following way.Suppose that the country exported R different agriculturalgoods and net export of the individual commodities wereE1, E2 ……..ER. Let E be the total net export of the country andm1¼E1/E, m2¼E2/E,..,mR¼ER/E, be the share of individual com-modities in total net export. Suppose that there are j¼1, 2 ….. nnumber of states in the country and sij, i¼1, 2 ….. R, j¼1, 2 …. nis the value share of crop i in total agricultural production ofstate j. Then the index of openness for the state j can beconstructed as

OPENj ¼ s1jm1þs2jm2þ :::þsRjmR:

� The amount of Government expenditure on agricultural educa-tion and research is normalized by dividing it total area underagricultural operation and is denoted as EDUR.

� Government (GSHARE) is measured by the proportion ofirrigated area under government canal irrigation.

� Agricultural credit (LOAN) is measured by the total amount ofcredit issued by rural banks and agricultural cooperatives peracre of cultivated area in the state.

� Crop diversification index (CD) is the inverse of the Hirshmann-Harfindahl index of concentration of land allocated todifferent crops.

� Rural Literacy Rate (RLIT) comes from the Census.� HYV is the percentage of the cultivated area using high yielding

varieties of seeds.� RAIN is the amount of annual rainfall in the state in a given

year.

Data used in this study have been collected from the differentissues of Statistical Abstracts published by Central StatisticalOrganization (CSO) of India, http://www.indianstat.com, Centerfor Monitoring the Indian Economy (CMIE), Agricultural Statistics ata Glance [14], and Indian Agriculture in Brief [13] published by theCentral Statistical Organization, different issues of Census of India[12], National Sample Survey (NSS) Reports, and FinancialAccounts, Government of India, Publication [15].

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