Agricultural Banking

Efficiency and Productivity in Indian Agriculture: A Stochastic Frontier Approach∗ Ayan Kumar Pujari† January 2005

Abstract This paper addresses the issues of technical efficiency, total factor productivity and its convergence for cereal crop production in Indian agriculture using district level data over a period of twenty-five years from thirteen major states. We estimate a Stochastic Frontier model to analyze technical efficiency after controlling for the district specific and climatic impact in the production of cereal crops. Our result documents that infrastructural (physical as well as social) development can raise efficiency in cereal production. The policy of license raj (1:4 policy) introduced in the banking sector has reduced efficiency. The estimated average efficiency scores for the Indian states show the varying nature of the relative performance of the states. The result from the calculated Malmquist index of total factor productivity (TFP) provides the evidence that efficiency change results in fluctuation of TFP change, although the share of technical change is substantial. The tests for conditional as well as unconditional convergence show that productivity in Indian districts tend to converge in case of wheat, rice, bajra and jowar; but not in case of maize and aggregate cereal crops. Key words: Efficiency, Total Factor Productivity, Convergence, India JEL Classification: D24, O13, Q10

∗ The

author is grateful to Prof. Kirit Parikh and Dr. Kausik Chaudhuri for their valuable suggestions during the preparation of this paper. † Research Scholar, IGIDR, Gen. A. K. Vaidya Marg, Goregaon (East), Mumbai - 400 065, INDIA. Phone +91-98924 27401, E-mail: [email protected]

1 Introduction This paper analyzes the production scenario in Indian agriculture from the efficiency and productivity point of view. Agriculture plays a pivotal role in Indian economy. Around one-fourth of total GDP comes from agriculture and allied activities, which makes it the largest contributor. This sector provides employment to nearly 70 percent of total workforce.1 In terms of export earnings also, the share of this sector is substantial. Apart from these, it provides raw and intermediate inputs to many industries. Thus, analysis of agricultural productivity and performance is important from the standpoint of economy-wide impact and hence it deserves to be one of the foci of policy makers. On the other hand, many of national objectives like poverty alleviation, eradication of unemployment and inequality are also interlinked with the development of the agricultural scenario in India. After the initiation of Five Year Plans, a number of agricultural policies have been proved to be helpful in improving the agricultural growth rate which was as low as 0.5 percent per annum prior to 1950 [Bhalla and Singh, 2001]. Large investments in irrigational infrastructure (though not sufficient for India as a whole) and the introduction of new seed-fertilizer technology during mid-1960s are two such policies that have altered the patterns and methods of agricultural production. The HYV (High Yielding Variety) technology was initially confined to Punjab, Haryana and some districts in western Uttar Pradesh. However, it became popular throughout India later. The same is the case with the use of fertilizers. During the inception of agricultural reforms, fertilizers were used only in the irrigated areas, but over time, the rain-fed areas also started using large amounts of modern fertilizers. The agricultural output in India largely depends on monsoon as nearly 60 per cent of area sown is dependent on rainfall. The introduction of new technology and machines, such as tractors, also has its own importance in the development of Indian agriculture. Increasing diversification of the cropping pattern has also contributed to the improvement in agricultural growth. 1 India

2004, Publication Division, Ministry of Information and Broadcasting, Government of India.

India, spanning a huge geographical area, comprises of different agro-climatic environment and resource endowments. These regional differences tend to get aggravated further because of the varying levels of investments in infrastructure and technological innovations. Several studies2 have mentioned the importance of regional differences in Indian agriculture. Despite these regional differences, it is observed that policies are not differentiated according to the need of the respective regions. A homogenous policy may not be effective due to these fundamental differences. This necessitates to analyze such differences which may provide more insights in making of appropriate policies. It is also important to observe how efficiently the resources are being used in different regions, considering the differences in terms of natural resources and endowments. Traditionally, production functions were used as tools for analyzing the production structure. The use of production function to analyze the role of inputs is strongly supported by the mainstream economists. However, due to problems in resource allocation, some of them feel that the cross sectional production functions are “under rewarding” in analyzing for which they do not hesitate to call it as “vulgar econometric work” [Kata [1990] pp 1]. An alternative approach, known as frontier approach is more general than a traditional production function approach, which postulates that the traditional system of analyzing production function is not appropriate since it assumes that all individual firms are technically efficient. Frontier production function relaxes the assumption of perfect efficiency in the production process and hence it is more realistic than an ordinary production function. Given the above situation, our paper is an attempt to estimate a stochastic frontier production function for five major crops in India using a district level data set. Apart from providing the input-output relationship, estimation of a stochastic production function at least serves two purposes: first the estimation of the efficiency scores highlight the efficiency part of Indian agriculture.3 Second, it also helps to analyze the role of those factors 2 Please 3 For

see Tedesse and Krishnamurthy [1997]. detail on this, please see Kalirajan and Shand [1999].

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which may be directly involved in the production process. However, these factors can exert some impacts in terms of the reducing inefficiency of the production purposes.After getting the estimates from the stochastic production function, we have constructed the total factor productivity and analyzed the issue of convergence in terms of total factor productivity. Our results document the following: first, apart from the conventional factors of production, the inter-regional disparity is substantial and climate has a major role to play in cereal production. Second, the physical and social infrastructural indicators like market density, road density, rural bank branch and literacy rate are found to have impact on technical efficiency. The policy of license raj (1:4 policy) in the banking sector, introduced in 1977, has reduced efficiency in our model. Third, the efficiency change results in fluctuation of TFP change, although the share of technical change is substantial. Finally, the tests for conditional as well as unconditional convergence show that Indian districts tend to converge in case of wheat, rice, bajra and jowar; but not in case of maize and aggregate cereal crops. The paper is organized as follows: Section 2 reviews the existing literature. Some of the conceptual issues regarding the production frontier are analyzed in Section 3. Section 4 discusses the data and the methodology. The empirical results are reported in Section 5. Section 6 concludes.

2 Literature Review Efficiency measurements have been attempted in Indian agriculture since 1970s [please see Lau and Yotopoulos [1971], Sidhu [1974], Junankar [1980], Battese and Coelli [1992, 1995], Datta and Joshi [1992], Shanmugam and Palanisami [1993], Tedesse and Krishnamurthy [1997], Kalirajan [1997] etc.]. Efficiency has been measured and decomposed into various components using both parametric as well as nonparametric methods. The two principal methods that have been employed to analyze the efficiency are Data En3

velopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), which involve mathematical programming and econometric methods, respectively. Kalirajan [1981, 1985], Battese and Coelli [1992, 1995], Tedesse and Krishnamurthy [1997], Mythili and Shanmugam [2000], Shanmugam [1994, 2000] are some of the studies that use SFA to analyze efficiency in Indian agriculture. Kalirajan [1981] points out that given the same access to inputs, the responsiveness of the small farmers to economic opportunities is the same as the case with the large farmers. His study is based on seventy farmers from Coimbatore district in the state of Tamil Nadu. Datta and Joshi [1992] document that the technical efficiency stands at eighty-four percent and sixty-six percent for wheat and rice respectively using the data on 120 farms from the district of Aligarh in Uttar Pradesh. Shanmugam [1994], using the data from Ramanathapuram district in Tamil Nadu, estimated a CobbDouglas production function for rice. He suggested that strengthening the farm extension services is necessary to bridge the gap between the farmers. Battese and Coelli [1995] performed a stochastic frontier analysis using a panel data for ten years. They documented that schooling increases efficiency while the age decreases it. Kalirajan [1997] suggests a methodology to obtain economic efficiency of firms using returns to scale. He documents that half of the rice sample farmers in Karnataka are economically efficient. Mythili and Shanmugam [2000] estimated a stochastic frontier production function for 234 rice farmers in Tamil Nadu. They obtained wide variation in technical efficiency, ranging from 46.5 percent to 96.7 percent. Shanmugam [2000] used the same methodology in case of rice farmers for Bihar. He shows the high elasticity of both: land and fertilizer. The technical efficiency ranges from 36.7 percent to 98.1 percent. As evident, most of the previous studies have analyzed single crops and the models are region specific, i.e., confined to one village or one district or one state using farm level dataset. Our study in an exception in this regard, namely, we use the SFA to analyze the inefficiency effects of districts in the production of cereal food grains in Indian agriculture using a panel data for two hundreds and eighty-one districts over a period of twenty-five years. We also try to model explicitly the role of some of the factors that may affect 4

inefficiency. Ranade [1986], Sidhu and Byerlee [1991], ?, Kumar and Rosegrant [1994], Rosegrant and Evenson [1992, 1993], Evenson et al. [1999], Desai and Namboodri [1997], Murgai [2001], Murgai et al. [2001] etc. are some of the important studied for analyzing the productivity in Indian agriculture. Almost all of them use the Tornqvist-Theil index to obtain productivity. Sidhu and Byerlee [1991] estimate a growth in TFP of 1.7 percent per annum using data from Punjab over the period 1972-1984. ? using the data from Haryana, Madhya Pradesh, Punjab, Rajasthan and Uttar Pradesh over the year 1970-71 to 1988-89, document that the research and extension services, share of machine labor in total labor, rainfall etc are positive contributor to TFP growth. However, literacy rate has a negative coefficient in explaining growth in TFP. Rosegrant and Evenson [1992] estimate 1.01 percent growth in TFP for India. Public research and extension and private inventions are the most important sources of growth in TFP in case of India. Rosegrant and Evenson [1993], using the data from 271 districts over the period 1956-87 shows that the growth in TFP for India stands at 1.01 percent per annum. Decomposition exercise presents that output growth contributes one-third of the growth in TFP. The remaining can be attributed to input growth, presence of markets, irrigation facility, literacy rate, use of HYV seeds augment TFP. Murgai [2001], correcting for bias in technical change measurement in case of Hicks non-neutral technology, shows that growth in TFP lies between 4 to 5 percent per annum. Evenson et al. [1999] show that the public agricultural research explains 30 percent of TFP growth. Investment in agricultural extension programs had substantial effect on growth in TFP. Improved rural markets, irrigation investments and modern inputs have also contributed to the growth in TFP. However, the Tornqvist-Theil index needs information about both: quantity and price. The alternative popular index in this area is the Malmquist index. In case of Malmquist index, it is possible to calculate productivity only with information on quantity. The other advantage of Malmquist index comes from the decomposition exercise, namely into technical change and efficiency change [F¨are et al (1994)]. Suhariyanto and Colin [2001] use 5

this approach to analyze agricultural productivity in 18 Asian countries. Coelli and Rao [2003] also use Malmquist index to analyze productivity in 93 developed and developing countries. In case of Indian agriculture, our study is the first attempt in this direction. McCunn and Huffman [2000] document the evidence for the β-convergence and clearly reject the presence of σ-convergence with the US agricultural data. Suhariyanto and Colin [2001] document evidence against convergence of agricultural TFP for for eighteen Asian countries using the data from 1965 to 1996. Coelli and Rao [2003] have considered 93 countries over the period 1980-2000 to analyze TFP. India posted a growth in TFP of 1.4 percent per annum. For India, they found that efficiency change to be 1.008 and technical change to be 1.006. In the context of convergence, they found that the countries that were below the frontier in 1980 have a TFP growth of 3.6 percent as against 1.2 percent for those countries that were on the frontier during the same period. Mukherjee and Kuroda [2003] address the convergence issue of TFP in 14 major states in India. They document the evidence for the β-convergence and clearly reject the presence of σ-convergence. They suggest that elimination of differences in infrastructure, research and development expenditure, spending on social services etc. would have a significant impact on the rate of convergence across different regions in India. Studies regarding the convergence issue in Indian agriculture at disaggregate level is absent. Our paper is also an attempt in this direction. Specifically, we address the following questions: How does the system of cereal production work in India? In other words, what are the important factors of production that govern the cereal production? Do the regional differences matter? What is the efficiency level of the system of cereal production in India and what are the factors that affect efficiency? What is the pattern of total factor productivity (TFP) and do the Indian districts converge in terms of their productivity? In the next section, we briefly explain the conceptual issues regarding technical inefficiency, productivity, their respective measurement procedures and convergence.

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3 Conceptual Issues Performance is a relative term which is measured by comparing it with a benchmark. This paper analyzes performances of districts in terms of technical efficiency and productivity for cereal production in India. Since the term ‘firm’ is more common in this kind of analysis, we will use it interchangeably with ‘district’. This section consists of two subsections. The first one deals with the concepts and measurement of efficiency and productivity, whereas the second subsection explains the concept of convergence.

3.1 Technical Efficiency and Productivity Efficiency and productivity are two important aspects to analyze performances of firms. Here, we briefly discuss their concepts and explain how they are different from each other.

3.1.1

Technical Efficiency (TE)

The concept of frontier is the core substance in analyzing efficiency/inefficiency, which is used as the benchmark to evaluate the performances. A frontier production function represents the maximum level of of outputs that can be produced conditional on various input levels. Therefore, this can be regarded as the underlying technology in the production process. The frontier production function postulates the existence of inefficiency in the process of production. A firm is said to be technically efficient if it operates on the frontier. The level of inefficiency is measured by the gap between the realized output and the corresponding frontier output, conditional on a particular level of input. A formal definition of technical efficiency would be ‘the ability and willingness of firms to produce the maximum possible output with a specified quantity of inputs, given the prevailing technology and environmental conditions. Figure 1 explains the concept of technical efficiency for a one input-one output case where x and y denote input and output respectively. In Fig. 1, OF 0 is the production frontier, all points on and below which are feasible. 7

The firms operating on OF 0 are considered as technically efficient (e. g., point B and point C), where as the firms operating below (e. g., at point A) are technically inefficient. TE at point A would be measured as TE= 0 TI= 1 − Ax Bx0 =

AB Bx0 .

Ax0 Bx0 .

Alternatively, technical inefficiency would be

Note that 0 < TE, TI < 1, since no firm can practically operate above

the frontier and TE+TI=1. Theoretical works of Koopmans (1951), Debreu (1951) and Shepard (1953)4 are the initial studies which discuss efficiency. However, productive efficiency was first measured empirically by Farrel (1957). The empirical research on efficiency involves in constructing a frontier (which envelops the data), as compared to production function (which intersects the data). There are two popular approaches to measure TE, such as Data Envelopment Analysis (DEA) and Stochastic Frontier (SF) Analysis. The basic idea behind both the approaches is to construct a frontier and then to obtain TE score on the basis of the gap between the realized output and the corresponding frontier output for each input combination. However, the fundamental difference between them is that the former is a non-parametric approach (uses mathematical programming), where as the later one is a parametric approach (uses econometric technique). The choice among these two alternative approaches depends upon the nature of problem at hand. The main advantages of SF over DEA is that DEA assumes all deviations from the frontier are due to inefficiency and it ignores the random factors affecting production process. Since the random factors are taken into account by SF models, it can accommodates the firms operating above the frontier (point D in Fig. 1) also. Here the random errors are greater than the corresponding inefficiency effects. Additionally, we can perform several statistical tests in SF analysis. In the present context, we have selected SF model to analyze efficiency in Indian agriculture for the simple reason that agriculture data, particularly in developing countries, are heavily influenced by measurement error and the effects of weather, natural calamities etc.5 However, this has been tested subsequently in our study. 4 Kumbhakar 5 Coelli,

and Lovell [2000], page 6. Rao and Battese (1998), page 219.

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3.1.2

Productivity

Productivity is defined as the ratio of outputs to inputs, where larger value of this ratio are associated with better performance. In the presence of a single input and a single output, productivity is a trivial measure, which is expressed as a ratio of output quantity to the respective input quantity. However, when there are more than one input (which is often the case) and output, we need an aggregative measures (as indices for inputs and outputs) to obtain a productivity ratio. Here, by productivity, we mean total factor productivity (TFP), which is a productivity measure involving all factors of production. In contrast to this, we can measure the partial productivity, such as labor productivity, land productivity (yield) etc. which are the traditional measures of productivity. These partial measures of productivity may provide a misleading indication of overall productivity if they are considered separately. In Figure 1, we can measure productivity at a particular data point as the slope of a line from the point to the origin. For example, productivity at point A is equal to the slope of the line OA, i. e.,

Ax0 Ox0 .

The more the slope, the more the productivity.

There are many ways to calculate productivity, however, we have used the most popular method (known as Malmquist index of TFP) to analyze productivity in our set up. Often, the terms productivity and efficiency are used interchangeably. However, they are not the same thing. It can be seen that even if all points on the frontier are technically efficient, there would be only one point (where a straight line from the origin is tangential to the frontier) that has the maximum productivity. Given a technology, each input level has a efficient point, where as we have only one point with highest productivity for that technology. In Fig. 1, point A is inefficient. The efficient point with same level of inputs is B. If there is a movement from A to B, there would be rise in both productivity as well as efficiency. However, with this technology, there is only one point, i.e., point C, where productivity is maximized. Moving from point B to C does not add to efficiency, but there is an improvement in productivity. Point C, in this case is known as the point of maximum possible productivity or the point of optimal scale. This difference between efficiency and

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productivity needs to be taken care of.

3.1.3

Modeling Inefficiency

As we have mentioned earlier DEA and SFA are two popular ways to measure efficiency. DEA was first used by Charnes, Cooper and Rhodes (1978). Since then a large number of papers have been extended and applied the DEA methodology. On the other hand, the stochastic frontier was independently proposed by Aigner and Schmidt (1977) and Meeusen and van den Broeck (1977). While the DEA approach postulates that all deviations of the realized output from the frontier level is are due to inefficiency, SF considers the effects of random factors also. The key difference between between an SF and a standard stochastic production function is that SF includes an additional non-negative error component to explain inefficiency which the standard production function does not. Several distributional assumption can be made regarding the one sided error term. The general practice has been to assume an exponential or a half normal distribution.6 SF approach has been extended to model the inefficiency effect also, where one can identify the factors governing the inefficiency of firms. Pitt and Lee [1981], Kalirajan [1981], Kalirajan and Shand [1989]7 adopt a two step procedure where the first step involves the estimation of frontier and prediction of efficiencies of the firms. The second step involves the estimation of a model where the predicted efficiencies are set to be a function of some explanatory variables. However, recently, developments have been done to estimate the production frontier along with the inefficiency model with the help of maximum likelihood (ML) approach. Kumbhakar, Ghosh and McGuckin (1991) and Reifchneider and Stevenson (1991) specified SF models where inefficiency effects were expressed as functions of some firm specific variables. Battese and Coelli [1995] extended these approach to accommodate panel data. Coelli et al. [1998] explain the efficiency and productivity analysis with DEA, SF as well as various indices to measure productiv6 In

our study we have assumed a half normal distribution. et al. [1998].

7 Coelli

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ity. Kumbhakar and Lovell [2000] provides an excellent exposition to stochastic frontier analysis. Consider an SF production function for panel data, defined as8 Yit = exp(xit β +Vit −Uit )

(1)

where Yit is the output of ith firm at t th observation, xit is a vector of inputs for ith firm at t th observation, β is a vector of parameters to be estimated, Vit s are random errors which are i.i.d. ∼ N(0, σ2v ), Uit s are the non-negative random variables distributed independently, associated with technical inefficiency, Vit and Uit are independent of each other and of the explanatory variables. Equation 1 alone does not explain the factors governing inefficiency. So we need to specify the inefficiency effect, Uit which is as follows in our analysis. Uit = zit δ + ωit

(2)

where zit is a vector of variables which explain the inefficiency effects in the model, δ is a vector of parameters to be estimated, ωit is defined by the truncation of the normal distribution with zero mean and variance σ2 , such that, the point of truncation is −zit δ; i. e., ωit ≥ −zit δ. These assumptions are consistent with Uit s being non-negative truncation of the N(zit δ, σ2 ) distribution. 8 Coelli

et al. [1998] have explained this model in more detail.

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Since TE of a firm is the ratio of realized output to the corresponding frontier output, conditional on the level of input, it is derived as follows Yit exp(xit +Vit ) exp(xit +Vit −Uit ) = exp(xit +Vit )

TEit =

(3)

= exp(−Uit ) = exp(−zit − ωit )

The parameters of the SF model, defined by Equation 1 and 2 can be estimated simultaneously by the method of ML.9

3.1.4

Measuring TFP

The Malmquist approach is the most popular approach to obtain TFP in the literature, which is based on the concept of distance functions. We can define an output distance function with period-t technology for a given output vector, y, and input vector, x, as dot (x, y) = min{δ : (y/δ, x) ∈ Production Set}, δ ≤ 1

(4)

The distance, δ, here represents the smallest factor, by which output needs to be deflated so as to be feasible with a given input vector, x, under period-t technology. Following F¨are et al (1994),10 the Malmquist TFP change index between period-s (base period) and period-t is given by d s (yt , xt ) dot (yt , xt ) . m0 (ys , xs , yt , xt ) = os do (ys , xs ) dot (ys , xs ) 

9 You

1 2

(5)

can find the derivation of the likelihood function and its partial derivative with respect to the parameters of the model in Battese and Coelli (1993). 10 Coelli, Rao and Battese, 1995, page 223.

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This can be expressed as the product of efficiency change (EC) and technical change (TC) as follows:  1 dot (yt , xt ) dos (yt , xt ) dos (ys , xs ) 2 m0 (ys , xs , yt , xt ) = s . = EC. TC do (ys , xs ) dot (yt , xt ) dot (ys , xs )

(6)

It is important to note that constant returns to scale (CRS)be imposed , otherwise the resulting measures may not properly reflect the TFP gains or losses resulting from scale effects [Coelli et al., 1998].

3.2

Convergence

There are two concepts of convergence, such as conditional and unconditional. The former is related to a cross-section study which focuses on the tendency of cross-sections with relatively low initial levels of productivity to grow faster than the cross-sections with higher level of initial productivity. On the other hand, unconditional convergence assumes cross-sections to have the same steady state over time. Conditional convergence is tested with the coefficient of the regression of growth rates on the initial levels of productivity, which can be expressed as follows: gi,t = α + βyi,0 + εi,t

(7)

where gi,t = T −1 (yi,t − yi,0 ) is the average growth rate of productivity of cross-section i, yi,0 is the initial level of productivity of cross-section i, εi,t is an error term with zero mean and constant variance and α and β are parameters to be estimated. If the estimate of β is found to be negative and significant, there is said to be Beta convergence (β-convergence). Another test for convergence, known as Sigma convergence (σ-convergence), holds if the cross-sectional standard deviations of the log of productivity index decrease over time. This investigates the tendency of productivity difference between countries to narrow over time. This can also be done be regressing the standard deviations of the cross-

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sections over time on a trend variable. A significant negative coefficient would provide the evidence of the σ-convergence. The test for conditional convergence is performed through the β-convergence, where as unconditional convergence test is done through the σ-convergence approach. The above two approaches are related to each other even though they illustrate different phenomenon. Sala-i-Martin [1996] shows that β-convergence is a necessary, but not the sufficient condition for σ-convergence.

4 Data and Methodology The data that we use in the paper comes from multiple sources. The main source is the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT) dataset. The ICRISAT provides informations for 281 districts (the smallest administrative units in India at which consistent and reliable data are available) in 13 major states in India. Two major states, Kerala and Assam are not covered in the dataset. The time span covered is from 1966-67 to 1994-95. The other sources we depend on data are Census India Info 2001 CD-ROM, http://www.indiastat.com, http://www-esd. worldbank/indian, Statistical Abstracts of several statesi and Statistical Tables Relating to Banks in India. A detailed description has been provided in the Appendix. We have used the the yields of the aggregate cereal crops and major cereal crops individually (wheat, rice, maize, bajra and jowar),11 as the dependent variables in the frontier estimation. We have also used informations on GIA (Gross Irrigated Area), GCA (Gross Cultivated/sown Area) and area under crops crops are measured by thousand hectares. Quantity of labor is the number of rural males whose primary job classifications are agricultural labor and cultivation. Fertilizers (consisting of nitrogen, Phosphorous and Potassium) are expressed in terms of tonnes. Quantity of bullock is the sum of cross-bred and 11 Yields

of crops are measured as the ratio of production of the crops to their respective area planted (tonnes/hectare).

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indigenous breeds cattle.12 Quantity of tractor is the number of four-wheeled machines (not tracked or walked behind two wheeled ones). All the inputs used in our analysis are in aggregate level.13 However, the crop wise data for yield of major crops only (wheat, rice, maize, bajra and jowar) have been used in this analysis. Some climatic variables has been introduced. The first one is the length of growing period (lgp).14 We have used monthly normal rain fall information normalized by their corresponding monthly potential evapo transpiration (pet).15 The output and the input variables (namely, irrigation, labor, fertilizers, bullock and tractors) are expressed in natural logarithms. The dependent variables are crop, wheat, rice, maize, bajra and jowar; which are obtained as log(Yieldc ), where c={total cereals, wheat, rice, maize, bajra and jowar} respectively. The independent variables have been normalized (to have a proper comparison) with respect to the gross cropped area (GCA). After transformation, the final set of inputs consists of irrigation index (I), labor index (L), fertilizer index (F), bullock index (Bu) and tractor index (Tr). Given the presence of regional heterogeneity as discussed previously, we have also used district dummy for each of the crops. The set of inputs are in aggregate level and same for all the crops.16 To model the inefficiency, we have considered several infrastructural variables, such as market density (ratio of total number of principal and sub-markets to district area), road density (ratio of road length to district area), rural bank branch density (ratio of rural bank branch to total bank branch) and literacy rate (for the population over 6 years). The data on bank branch is at the state level.17 The literacy rate data is from Census of India. We 12 For

cross-bred cattle, an adult is over 2.5 years and for indigenous it is over 3 years. only for all crops, not crop wise. 14 lgp is a state variable which means that it has been observed once for each districts, i. e., for a district, it is constant over time. 15 pet is the amount of water transpired in a given time by a short green crop, completely shading the ground, of uniform height and with adequate water status in the soil profile. Under high rates of pet, relatively high amounts of soil moisture needs to be available to crops, else a water deficit occurs, reducing crop growth rate. Irrigation rates can be lowered if pet is low, i. e., where the rainfall index in our analysis is high. 16 Since crop-wise information are not available for these inputs. 17 This is collected from various issues of Statistical Tables Relating to Banks in India, published by 13 Available

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linearly interpolate the data for in between Census years. After the nationalization of banks in 1969, the Reserve Bank of India in 1977, introduced a policy (which we term as License Raj) in order to promote rural banking. This licensing policy was aimed at forcing the banks willing to open a branch in an already banked location to open four branches in unbanked locations. The policy came to an end in 1991. In order to capture the impact, we have introduced a dummy variable, taking the value 1 between 1977 and 1991. In order to find out whether this policy has time varying impact or not, we construct a break trend which starts at 1977 and ends at 1991 (following Burgess et al. [2004]). The motivation of using this trend break is to capture the differential impact of pre-licence raj, licence raj and post-licence raj policy period. In line with Burgess et al. [2004], we also introduce an interaction term (trendbranch), which is the product of the break trend and the bank branch variables. This linear trend relationship between state’s initial financial development and rural branch expansion has been used as an instrument for the number of rural bank branches created in unbanked location as a result of the 1:4 policy. Burgess and Pande [2003] find that rural branch expansion has stimulated secondary and tertiary sector output at the expense of agricultural output and employment. We also incorporate a trend component in the inefficiency equation to analyze the overall change in efficiency over the covered period. A brief description of variable construction has been presented in Table 1. A Translog specification has been used here to estimate the stochastic frontier production function which takes the following form: n n 1 n 2 y = β0 + βt t + βtt t + ∑ βi xi + ∑ βii xi + ∑ ∑ γi j xi x j 2 i=1 i=1 i=1 j=1 2

n

(8)

where y is the output index and xi is the ith input used for the production. Note that all y and xi are in logarithmic terms. The above relation approaches to a CD form if and only if βii = γi j = 0 and hence is more general than the popularly used CD form. In this model, Reserve Bank of India.

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t is the time trend, which is supposed to capture the technical change during the study period. We also use t 2 to take into account the non-linear impact of the trend variable. The trend variable in this function accounts for Hicksian neutral technological change. A Translog function is quadratic in nature, as it is clear from its specification. A significant coefficient of the square of a particular input would mean that it affects the production in a non-linear fashion and similarly a significant coefficient of an interaction term (say, xi x j ) implies that the ith and jth inputs can affect the output by interacting with each other. Given the nature of the translog production function, we calculate the marginal effects (ME) of any input xi on any dependent variable Y as follows: n δy = βi + βii xi + ∑ γi j x j δxi j=1

(9)

These ME are the respective partial elasticities. A positive coefficient of βii means that the ME of xi on y increases with an increase in xi , i.e., the additional y for one per cent increase in xi is higher with an already high level of xi as compared to a low level of xi . In other words, the effect of xi on y increases at an increasing rate. With the above expression, we can measure the ME exhibited by different factors of production on the output in our system. Our inefficiency model uses a linear specification which can be expressed as follows: n

Uit = δ0 + δ1t + ∑ δi Zit + ωit

(10)

i=2

where t is the overall trend. The vector Zit consists of the variables explained above. With the above specification, we have estimated the SF model (Equation 1 and 2 simultaneously) by the method of ML using FRONTIER 4.1c.18 Subsequently a number of hypothesis have been tested with likelihood ratio (LR) test, which provides justification 18 A

computer program, developed by Coelli [1996].

17

for our study. As we have mentioned earlier, six different models have been estimated, one for each crops and an aggregate model.

5 Empirical Results In this section, first we will present the hypotheses testing which have been performed to select our models. The summary of LR tests for the general models for all the crops has been given in Table 2. We have presented the test results only for the aggregate cereal crop model.19 The null hypothesis that the inefficiency effects are absent in the model (i,e,. H0 : γ = δi = 0 for i = 0, 1, · · · , 7) is rejected. Further, the null hypothesis H0 : γ = 0 (inefficiency effects are not random) is also rejected. This signifies the use of SF approach over a deterministic approach. This also supports the presumption of uncertainties (due to irregular monsoon, drought, flood etc.) in Indian agriculture. The rejection of the null hypothesis H0 = δi = 0 for i = 1, · · · , 7 clarifies that they are well explaining the inefficiency model. Rejection of the next hypothesis (H0 : No dummy effect) suggests the use of district dummy to control for the district specific unobserved effects. Finally, the last hypothesis gives the evidence for using Translog specification in stead of a CD specification in our model. All hypothesis are rejected at all conventional level of significance. On the basis of the above results, we estimate our models and report the results in the next sub-section. This section has been divided into four subsections. Subsection 1 reports the estimation results. The marginal effects at the mean level has been discussed in Subsection 2. Subsection 3 presents the inefficiency comparison among states. TFP calculation and its growth have been explained in Subsection 4 and Subsection 5 deals with the convergence result. 19 The

results are same for all the models.

18

5.1 Estimation Results Table 3 presents the estimation results of the stochastic frontier models. It is observed that time trend has positive impact in most of the cases both in linear as well as non-linear sense. The variable ‘lgp’ is found to be an important factor in the production process. The indices for the climate variable are also found to play an important role in our models. To save space, the coefficients for dummy variables are not reported here.20 We have also calculated the marginal effects of the conventional inputs in the next subsection. In the inefficiency model, a negative sign suggests negative impact on inefficiency (alternatively, positive impact on efficiency). Table 4 reports the coefficient estimates of the inefficiency models in each of the cereal crops. The coefficients of time variable show that there has been significant improvement in efficiency over time.21 In the cereal production, it is observed that the physical infrastructure variables such as presence of markets, road length and bank branches do have increased efficency. All of them are found to have negative coefficients which are significant. This is true for individual crops also, with some exceptions. The social infrastructural variable (literacy rate) in the case of aggregate cereal production is showing positive sign, however, the impact is insignificant. This is also true in case of bajra and jowar. However, in case of rice and maize, it yields negative significant coefficient. In case of the wheat, the sign of the literacy rate variable is postive and significant. The impact of license raj dummy is of mixed nature. Although, the coefficient is negative and significant in case of aggregate crop, it is positive in four out of five cases in crop-wise estimation. The break trend is clearly showing that there has been a decline in efficiency during this period in case of all the crops. This kind of negative impact on efficiency can be attributed to the pressure on banks due to this 1:4 license policy. The banks were being set up in those areas where there was hardly any scope or incentives for the banks. This result is consistent with that of Burgess and Pande [2003]. The 20 Interested 21 Except

readers are requested to obtain them from the author. in the case of wheat production.

19

interaction of the break trend with the rural bank branch, however, has shown positive impact on efficiency. This shows that although the policy of 1:4 reduces efficiency, the expansion of rural branches in unbanked location as such raises efficiency in cereal crop production, may be by easing the credit availability source for the rural farmers. This positive impact of the interaction of the trend break with the rural bank branch is the result of the incentives and scope being provided to the farmers. Burgess et al. [2004] also provide the evidence that the instrument for number of rural bank branches have reduced poverty. Therefore, licence raj policy has influenced Indian agriculture in two different ways. The direct (negative) impact may not be so strong to eliminate the indirect (positive) impact on efficiency. However, this issue is beyond the scope of our paper.

5.2

Marginal Effects

Using Equation 2, we have calculated the marginal effects (ME) for all the conventional inputs (i.e., I, L, F, Bu and Tr) used in the system. We compute the ME using the mean values of the inputs. It is clear from Equation 2 that the ME are nothing but the corresponding partial elasticities. Therefore, ME of an input xi on the output Y gives the responsiveness of the output Y to one percent change in the input xi . We have presented the marginal effects (or partial elasticities) in Table 5. It is clear from this result that ME are more or less same in all the models in terms of their sign. Irrigation has positive impact on yields. The sign is found to be negative in case of bajra and jowar. This might be due to the fact that irrigation is not a major factor in the production of these crops. Other inputs like fertilizer, bullock and tractor show their respective marginal effects to be positive, except few cases. This implies that thee inputs have been helpful in raising the yields of the cereal crops. The only variable which has a consistent negative impact throughout is labor.22 This result indicates that there is a need to shift a part of labor force from these activities to some other productive activities. Dev [2002] also suggests that there should be shift of 22 In

case of rice, however, it is positive.

20

labor force from agriculture to non-agriculture sector as the labor productivity in the later sector is 6.7 times that of the former one. Such shift can help to reduce the gap among the sectors and hence can be a solution to remove inequality from the Indian economy.

5.3 Efficiency Comparison The state ranking has been presented in Table 6. Looking at the state ranking in the aggregate crop model, we find that Punjab, Uttar Pradesh and Haryana are among the best performers, where as Rajasthan, Maharashtra and Gujarat are the states having low efficiency scores.23 The ranking of the best performer states is more or less same in the production of wheat. This clearly shows the efficiency improvement of these states due to Green Revolution. However, in the case of wheat production, Andhra Pradesh, Karnataka and Tamil Nadu are the states with low efficiency scores. The ranking in case of rice reveals that the rice growing states like Tamil Nadu, Andhra Pradesh and West Bengal are found to have more than the average efficiency. Punjab has also performed well in rice production. In the production of bajra and jowar, states like Madhya Pradesh, Karnataka and Andhra Pradesh are performing well, where as states like Uttar Pradesh, Haryana, Rajasthan etc. are among the poor performers. The average efficiency in the case of aggregate cereal crop is reported to be 0.82, where as these figures stand at 0.83, 0.78, 0.74, 0.72 and 0.73 for the production of wheat, rice, maize, bajra and jowar respectively. The mean efficiency in rice production is reported to be 0.83 by Tedesse and Krishnamurthy [1997]. We found few farm level studies related to efficiency in Rice production (please see Datta and Joshi [1992], Shanmugam and Palanisami [1993], and Shanmugam [1994], where as other crops have hardly been studied individually. These studies report the mean efficiency in Rice production for farms in Tamil Nadu, Uttar Pradesh and Ramanathapuram district of Tamil Nadu as 0.66, 0.75 23 Note that West Bengal has been excluded from estimation in aggregate cereal crop model due to missing

observation problem. Similarly, Bihar is excluded from bajra and jowar.

21

and 0.82 respectively. All the above follow DEA approach to obtain the TE level. So, our efficiency score for rice production does not deviate much from those of earlier studies. We are not able to perform such comparison in case of other crops as there exist no previous studies. We also found that the percentage of districts below the average level of efficiency are respectively 43 percent, 38 percent, 41 percent, 49 percent, 53 percent and 40 percent in the production of cereal crops, wheat, rice, maize, bajra and jowar. This reflects further scope to raise cereal production without altering the present input structure. Therefore, policy makers should formulate relevant policies to train the farmers so that they are able to exploit the existing resources to produce more.

5.4 TFP Index and its Growth In our analysis we obtain Malmquist index of TFP as the product of EC and TC. Since dot (xi,t , yi,t ) = TEi,t , we calculate EC =

TEi,t TEi,t−1 .

On the other hand, TC can be calculated

from the estimated coefficients as follows:  0.5  ∆ ∆ TC = 1 + f (xis , s, β) 1 + f (xit ,t, β) ∆s ∆t The indices of EC and TC are then multiplied to get a Malmquist TFP index as defined in Equation 6. The TFP index along with two components (EC and TC) are shown in Figure 2 for the aggregate cereal crop model. The pattern of TC, EC and TFPC are same across the crops. From Figure 2, we can infer that both technical change (TC) and efficiency change (EC) contribute significantly to TFP change in cereal production. But EC only generates fluctuation in TFPC. TC is almost constant through out the study period. In figure 3, we show the TFP growth for the same model. It is clear from the figure that there has been large drop in productivity during a number of years which are the years of drought as reported in http://www.csre.iitb.ac.in/rn/resume/ drought/subcontinent.html. Rosegrant and Evenson [1993] also find the same 22

kind of result. They attribute the fluctuation in TFP mainly to fluctuation in output, as they found the total input use to increase smoothly over time. Contrast to their average TFP growth of 1.3 per cent per annum, we found an estimate of 1.9 per cent per annum. The difference may be due to the fact that they consider ten more minor crops in addition to the five major crops that we consider.

5.5 Results of Convergence Tests Following the findings of Sala-i-Martin [1996],24 we first test for the presence of βconvergence before testing for σ-convergence. The regression coefficient obtained from Equation 7 document the presence of β-convergence only in case of rice, bajra and jowar. In case of wheat, the sign of the coefficient is positive, but insignificant.25 Hence, we conclude that in case of rice, bajra and jowar, Indian districts are converging conditional on their initial TFP. For these four crops (wheat, rice, bajra and jowar), we check for the σ-convergence. Here we need to regress the standard deviations of log(productivity) to a time trend. This regression generates an negative but insignificant coefficient for the aggregate model.26 However, the coefficients are negative and significant in case of individual cereal crops having coefficients -0.002, -0.01, -0.01 and -0.005 for wheat, rice, maize, bajra and jowar respectively.27 Thus we find evidence in favor of β convergence as well as σ-convergence in case of wheat, rice, bajra and jowar, but not in case of maize and aggregate cereal crops. We can compare our convergence with that of Mukherjee and Kuroda [2003]. In their state level study, they document the evidence for the β-convergence and clearly reject the presence of σ-convergence. McCunn and Huffman [2000] also document the same result with the US agricultural data. 24 β-convergence

is a necessary, but not the sufficient condition for σ-convergence. coefficients are 0.108, 0.007, -0.206, 0.051, -0.382 and -0.016 for aggregate cereal crop, wheat, rice, maize, bajra and jowar respectively. 26 The coefficient is found to be 0.001. 27 The coefficient in case of Jowar is significant at 10 percent level of significance where as all other are found to be significant at 5 percent or less than 5 percent levels. 25 The

23

6 Conclusion This paper addresses the issues of technical efficiency, total factor productivity and its convergence for cereal crop production in Indian agriculture using data for 281 districts from 13 major state. We estimate a stochastic frontier model to analyze technical efficiency, controlling for the district specific and climatic impact in the production of cereal crops as a whole as well as five major cereal crops (wheat, rice, maize, bajra and jowar). The marginal effects of factors like irrigation, labor, fertilizer, bullock and tractor have also been calculated after the estimation. These results show that all the factors other than labor help to improve production. We also find that climate has a major role to play in cereal production. Apart from that, the inter-regional disparities (incorporated in terms of district dummies) are also substantial in Indian agriculture. In order to explain the factors responsible for inefficiency, we consider some infrastructural indicators like market density, road density, rural bank branch and literacy rate. These factors are found to have positive impact on technical efficiency which implies that infrastructural development can raise efficiency in cereal production. The policy of license raj (1:4 policy) in the banking sector has reduced efficiency in our model. This result is found to be consistent with that of Burgess and Pande [2003]. Further, we have calculated Malmquist index of total factor productivity (TFP) using the results from the frontier estimation. We find that efficiency change results in fluctuation in TFP change although share of technical change is substantial. We perform tests for conditional as well as unconditional convergence using the standard techniques of β and σ convergence respectively. The tests show that Indian districts tend to converge in case of wheat, rice, bajra and jowar; but not in case of maize and aggregate cereal crops. From our study, we conjecture that policy makers should try to improve the infrastructure base (both physical as well as social), specially in rural areas, which is crucial for making Indian agriculture more efficient. This can be possible since there is a large scope for exploiting the available resource base in an optimal way. Investment in techno-

24

logical improvement, research and development would be key to improve the agricultural situation in India. We also suggest that policy should be differentiated, keeping the interregional differences in mind. This would help not only to make different regions efficient, but also they will be able to converge with each other in terms of their productivity. This can help to remove inequalities among regions within agriculture sector as well as across different sectors.

25

References Battese, G. E. and Tim J. Coelli (1992). ‘Frontier production functions, technical efficiency and panel data: With application to Paddy farmers in India’. Journal of Productivity Analysis 3(1-2), 513–169. Battese, G. E. and Tim J. Coelli (1995). ‘A model for technical inefficiency effects in a stochastic frontier production function for panel data’. Empirical Economics 20(2), 325–332. Bhalla, T. and G. Singh (2001). Indian Agriculture: Four Decades of Development. Sage Publication Pvt. Ltd.. India. Burgess, R. and Rohini Pande (2003). ‘Do rural banks matter? Evidence from the Indian social banking experiment’. STICERD-Development Economic Papers 40, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. Burgess, R., Rohini Pande and Grace Wong (2004). ‘Banking for the poor: Evidence from India’. http://economy.lse.ac.uk/staff/rburgess/wp/ jeeabankindia.pdf. Coelli, T. J. (1996). ‘A guide to FRONTIER Version 4.1: A computer program for frontier production function and cost function estimation’. CEPA Working Paper 96/08. Coelli, T. J. and D. S. Prasad Rao (2003). ‘Total factor productivity growth in agriculture: A Malmquist index analysis of 93 countries, 1980-2000’. CEPA Working Paper No. 02/2003. Coelli, T. J., D. S. P. Rao and G. E. Battese (1998). An Introduction to Efficiency and Productivity Analysis. Kluwer Academic. Datta, K. K. and P. K. Joshi (1992). ‘Economic efficiencies and land augmentation to

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increase agricultural production: A comparative analysis for investment priorities’. Indian Journal of Agricultural Economics 47(3), 468–476. Desai, B. M. and N. V. Namboodri (1997). ‘Determinants of total factor productivity in Indian agriculture’. Economic and Political Weekly XXXII(52), A–165. Dev, M. (2002). Reforms and agricultural development in India. In the book ‘Agriculture in India and Maharashtra: Issues and Prospects’, MEDC Monthly Economic Digest for Business Executives. Evenson, R. E., Carl E. Pray and Mark W. Rosegrant (1999). Agricultural research and productivity growth in India. IFPRI Research Report 1099. International Food Policy Research Institute. Washington DC, USA. Junankar, P. N. (1980). ‘Tests of the profit maximisation hypothesis: A study of Indian agriculture’. Journal of Development Studies 16(2), 186–203. Kalirajan, K. P. (1981). ‘The economic efficiency of farmers growing high yielding irrigated Rice in India’. American Journal of Agricultural Economics 63(3), 566–570. Kalirajan, K. P. (1985). ‘On measuring absolute technical and allocative efficiency’. Sankhya (The Indian Journal of Statistics) 47(B), 385. Kalirajan, K. P. (1997). ‘A measure of economic efficiency using returns to scale’. Economic Letters 56(3), 253–257. Kalirajan, K. P. and R. T. Shand (1989). ‘A generalized measure of technical efficiency’. Applied Economics 21(1), 25–34. Kalirajan, K. P. and R. T. Shand (1999). Stochastic frontier production functions and technical efficiency measurements: A review. In K. P. Kalirajan and W. Yanrui (Eds.). ‘Productivity and Growth in Chinese Agriculture’. McMillan Press Ltd., Great Britain. Kata, V. R. (1990). Agricultural Production Function: An Appraisal. Ajanta. India. 27

Kumar, P. and M. W. Rosegrant (1994). ‘Productivity and sources of growth for Rice in India’. Economic and Political Weekly 29(53), 183–188. Kumbhakar, S. C. and C. A. K. Lovell (2000). Stochastic Frontier Analysis. Cambridge University Press. Lau, L. J. and Pan A. Yotopoulos (1971). ‘A test for relative efficiency and application to Indian agriculture’. American Economic Review 61, 94–109. McCunn, A. and W. Huffman (2000). ‘Convergence in US productivity growth for agriculture: Implications of interstate research spillovers for funding agricultural research’. American Journal of Economics 82(2), 370–388. Mukherjee, A. N. and Y. Kuroda (2003). ‘Productivity growth in indian agriculture: Is there evidence of convergence across states?’. Applied Economics 29(1), 43–53. Murgai, R. (2001). ‘The Green Revolution and the productivity paradox’. Agricultural Economics 25, 199–209. Murgai, R., Mubarik Ali and Derek Byerlee (2001). ‘Productivity growth and sustainability in post-green revolution agriculture: The case of the Indian and Pakistan Punjabs’. The World Bank Research Observer 16(2), 199–218. Mythili, G. and K. R. Shanmugam (2000). ‘Technical efficiency of Rice growers in Tamil Nadu: A survey based on panel data’. Indian Journal of Agricultural Economics 55(1), 15–25. Pitt, M. M. and Lung Fei Lee (1981). ‘The measurement and sources of technical inefficiency in the Indonesian weaving industry’. Journal of Development Economics 9(1), 43–64. Ranade, C. G. (1986). ‘Growth of productivity in Indian agriculture: Some unified components of Dharam Narain’s work’. Economic and Political Weekly XXI(25), A–65. 28

Rosegrant, M. W. and R. E. Evenson (1992). ‘Agricultural productivity and sources of growth in South Asia’. American Journal of Agricultural Economics 74, 757–761. Rosegrant, M. W. and R. E. Evenson (1993). ‘Agricultural productivity growth in Pakistan and India: A comparative analysis’. Pakistan Development Review 32, 433–451. Sala-i-Martin, X. (1996). ‘Regional cohesion: Evidence and theories of regional growth and convergence’. European Economic Review 49, 1325–1352. Shanmugam, K. R. (2000). ‘Technical efficiency of Rice grower in Bihar’. Indian Journal of Applied Economics 8(4), 377–389. Shanmugam, T. R. (1994). ‘Measurement of technical efficiency in Rice production’. Margin pp. 756–762. Shanmugam, T. R. and K. Palanisami (1993). ‘Measurement of economic efficiencyFrontier function approach’. Journal of Indian Society of Agricultural Statistics 45(2), 235–42. Sidhu, D. S. and D. Byerlee (1991). ‘Technical change and Wheat productivity in postgreen revolution Punjab’. Economic and Political Weekly 26(52), A159–A166. Sidhu, S. S. (1974). ‘Relative efficiency in Wheat production in the Indian Punjab’. American Economic Review 64(2), 742–751. Suhariyanto, K. and T. Colin (2001). ‘Asian agricultural productivity and convergence’. Journal of Agricultural Economics 52(3), 96–110. Tedesse, B. and S. Krishnamurthy (1997). ‘Technical efficiency in Paddy farms of Tamil Nadu: An analysis based on farm size and ecological zone’. Applied Economics 16, 185–192.

29

Tables Table 1: Construction of the variables Variables

Description

W R M B J GCA I L F Bu Tr

log(yield of wheat) log(yield of rice ) log(yield of maize) log(yield of bajra) log(yield of jowar) Gross Cultivated Area log(Gross Irrigated Area/ GCA ) log(no. of man days/ GCA ) log(total fertilizers(NPK)/ GCA ) log(no. of bullocks/ GCA ) log(no. of tractors/ GCA )

market density road density bank branch

Total no. of markets/ District area Road length/ District area No. of rural branches/ Total branches

a The variable bank branch is a state level variable.

Table 2: Hypothesis Testing for Model Selection Sl. Null no. Hypothses 1. 2. 3. 4. 5.

LR Statistics

Degree of Freedom

p-values

H0 : γ = δ0 = · · · = δ3 = 0 2363.133 H0 : δ1 = · · · = δ5 = 0 366.328 H0 : γ = 0 458.497 H0 : No dummy effect 2938.103 H0 : CD is better than Translog 330.042

10 7 1 263 16

0.000 0.000 0.000 0.000 0.000

a This table is for the aggregate cereal crop model. However, the test results are same

for all the individual crops too.

30

Table 3: Estimates of the Models variables cons time (t) irrigation (I) labor (L) fertilizer (F) bullock (Bu) tractor (Tr) t2 I2 L2 F2 Bu2 Tr2 IL IF Ibu Itr LF Lbu LTr Fbu FTr BuTr lgp c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12

crop

wheat

rice

maize

bajra

jowar

-0.105 -3.E-04 -0.216 0.166 -0.113 0.013 0.196* 4.E-04* 0.076* -0.050 0.016 0.008* 0.002 0.072* 0.021* -3.E-04 -0.001 0.017 -0.008 -0.027 0.008 0.001 -0.002 0.051* -2.624* -35.855* -111.170* 52.664* -11.541* 5.140* 6.920* 1.414* -8.274* -10.030* 11.174* 13.001*

0.939 0.001 0.031 0.148 0.394* 0.437* 0.187 0.001 0.009 0.060 0.001 0.013* 0.011 0.033 0.032 0.034 0.002 0.076 0.048 0.043 0.022 0.003 0.006 0.008* 1.735* 1.060* 2.934* 5.097* 1.309* 0.378 0.227 0.121 0.222 0.280 0.239 20.267*

-0.691 0.020* 0.166 -0.101 -0.283* 0.110 -0.443* -2.E-04* 0.056* -0.023 -0.007 0.002 0.010* -0.015 0.018* 0.009 -0.008 0.032 -0.029 0.066* 0.025* 0.016* -0.003 0.008* -1.313* 5.924 * -6.360* -0.974 1.285 * 1.103 * 0.154 0.207 -0.324* -0.007 -1.543* -3.398*

26.000* 0.019* -0.419 -1.445* -0.489* -0.452* -0.019 -3.E-04 -0.047 0.134 -0.030* 0.001 0.007 0.095* 0.038* -0.051* -0.002 0.067* 0.037 -0.004 0.036* 0.006 0.008 -0.036* -15.750* 38.254 * -34.450* -92.248* 60.171* -5.332* 2.401* -4.624* 2.068* -10.321* -3.150* -12.676*

-35.146* 0.020* -3.041* -1.874* 0.694* -0.063 0.591* -1.E-05 -0.166* 0.356* -0.025 0.031* 3.E-04 0.402* 0.046* 0.019 -0.032* -0.085* 0.011 -0.075* -0.001 0.028* -0.040* 0.061* 6.352* 17.070* -69.736* 54.300* 46.012* -10.117* 2.322* 4.327* 12.191* 1.041* -43.531* 36.855*

0.246 0.028* -0.664 0.317 -0.018 -0.291 0.236 -5.E-04* -0.098* -0.109 -0.030 0.017* 0.005 0.075 0.035 -0.027 -0.019 0.008 0.021 -0.032 0.027 0.028* -0.021 0.001 -2.709* 0.344 -0.968 -0.092 -0.838 0.320 0.197 0.076 -0.720* -0.224 -0.439 -1.630*

* indicates that the co-efficient is significant at 5 percent level of significance.

31

Table 4: Estimates of the Inefficiency Models variables

crop

wheat

rice

maize

bajra

jowar

constant time market density road density bank branch literacy rate license raj dummy trend break trendbranch σ2 γ

1.177* -0.019* -77.207* -1.412* -4.046* 0.024 -0.570* 0.294* -0.359* 0.492* 0.987*

0.599 1.294* 0.056 195.987* 1.125* 6.575* 0.339 0.382 0.008 0.536* 0.968*

-3.130* -0.081* -74.624* -2.213* 0.942 -0.547* 0.658* 0.636* -1.081* 1.532* 0.990*

1.146* -0.122* -91.534* -1.381* -6.056* -0.387* 0.511* 0.521* -0.682* 1.562* 0.972*

-3.463* -0.099* -92.850* -2.974* 2.158* 0.210 0.350* 0.522* -0.760* 2.148* 0.979*

-9.384* -0.319* -4.919 -1.174* 9.233* 0.525 -0.590 1.509* -2.310* 4.012* 0.992*

log likelihood no. of observations no. of districts

929.39 3592 264

556.37 5082 259

-546.86 5401 271

-2074.82 5193 268

-1979.28 4039 212

-1930.68 4748 236

* indicates that the co-efficient is significant at 5 percent level of significance.

Table 5: Marginal Effects Inputs

crop

wheat

rice

Irrigation 0.173 Labor -0.272 Fertilizer 0.059 Bullock 0.030 Tractor 0.021

0.519 0.991 0.952 0.832 0.505

0.093 -0.278 0.020 0.001 0.028

32

maize

bajra

jowar

0.089 -0.005 -0.080 -0.296 -0.433 -0.358 -0.001 0.017 0.044 -0.012 0.125 0.059 0.022 0.032 0.035

Table 6: Efficiency scores of the states State Name

crop

wheat

rice

maize

bajra

jowar

Andhra Pradesh Bihar Gujarat Haryana Karnataka Madhya Pradesh Maharashtra Orissa Punjab Rajasthan Tamil Nadu Uttar Pradesh West Bengal

0.84 0.87 0.75 0.90 0.84 0.83 0.76 0.89 0.93 0.78 0.83 0.91

0.77 0.82 0.81 0.87 0.73 0.84 0.77 0.82 0.90 0.84 0.65 0.87 0.78

0.83 0.80 0.71 0.81 0.79 0.77 0.72 0.82 0.86 0.67 0.83 0.79 0.83

0.73 0.77 0.71 0.75 0.78 0.78 0.67 0.81 0.81 0.72 0.74 0.74 0.71

0.72

0.78

0.72 0.71 0.73 0.73 0.72 0.72 0.70 0.71 0.72 0.71

0.68 0.69 0.75 0.78 0.74 0.74 0.73 0.65 0.73 0.72

Mean Efficiency

0.82

0.83

0.78

0.74

0.72

0.73

a Note that West Bengal is excluded from the aggregate cereal crop model,

bajra and jowar. Similarly, Bihar is excluded from bajra and jowar. This exclusion is because of missing data problem.

Figures 6

y



Dp



   pp pp  pp Bp  pp   pp , p , ppp  pppp p , p  ppp  pp , pp  ppp  pp , C s ppp pp p ppp ,,   ppp pp pp A ,   pppp pp , pp   pp , pppp   pp ,ppp pp  , pppp pp pp p  , pp pp pp  , ppp pp p , p  pp p pp , pp , pp pp p pp p , pp pp p p   ,

O

x1

x0

F0

-

x

Figure 1: Efficiency and Productivity 33

-0.05

34

-0.1

-0.15

-0.2

Year

crop

Figure 3: TFP Growth 19 9

19 9

19 9

19 9

19 9

19 8

19 8

19 8

19 8

0.05

0

19 9

19 8

19 8

19 8

19 8

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19 7

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19 7

19 7

19 7

19 7

19 7

19 7

19 9

0.1

4

0.15

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0.2

3

0.25

19 9

Figure 2: TFP Change and its components

2

TFP

19 9

year

1

0

9

8

7

6

5

4

TC

19 8

3

2

1

0

9

8

7

6

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2

EC

19 8

19 8

19 8

19 8

19 8

19 7

19 7

19 7

19 7

19 7

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19 7

19 7

Grwoth Rate (%)

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

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3.5

3

2.5

2

1.5

1

0.5

0

Appendix Explanation for Data We have made some adjustments to ICRISAT data using data from several State Statistical Abstract, Census India Info 2001 CD-ROM, http://www.indiastat.com and http://www-esd.worldbank/indian, which are consistent. The adjustments are as follows: • Production and area data are not available for some states for some particular years. We obtained some of them from various Statistical Abstract of the States and www. indiastat.com. Then we construct our dependent variables as the yields (expressed as tons/hectare) of respective crops. • GIA (Gross Irrigated Area), GCA (Gross Cultivated Area), Area under HYV cultivation for individual crops are expressed in terms of thousand hectares. • The labor data for 1971, 1981 and 1991 (partially) are available in ICRISAT dataset. We use the labor variable for 1991 and 2001 census from Census Info 2001 CD ROM. For the observations between the census years, we use the method of linear interpolation, following ‘India Agriculture and Climate Dataset’. Labor variable is the sum of male agricultural labor and male cultivators. • Fertilizers are expressed in terms of tons which is the sum of nitrogen, phosphorus and potassium used for cultivation. • The recent data for bullocks and tractors are obtained from Statistical Abstracts of the States and www.indiastat.com. Note that that livestock census years are not the same across states. In case of missing observations, we use the method of linear interpolation. Bullock is defined as the sum of cross-bred (adult over 2.5 years) and indigenous (adult over 3 years). • lgp (length of growing period) is the period when the moisture in the soil is adequate enough to support plant growth. • ‘pet’ (potential evapotranspiration) is not available for Kanyakumari district. Therefore, ‘pet’ for an adjacent district (Tirunelvelli) is used for it. In our analysis, monthly ‘pet’ is used to normalize respective rainfall to get the monthly climate variables (c1 to c12 in our paper). • Information on bank branches have been collected from various issues of ‘Statistical Tables Relating to Banks in India’, published by Reserve Bank of India.

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