Analysis of Rice Productivity and Sources of Growth in India

Abstract

The present study analysed the temporal pattern in India’s rice production and sources of productivity growth. The study used data from the cost of cultivation surveys for 10 major rice-producing states for the period 1990/91–2012/13 for analysing the sources of productivity growth. The analysis of growth performance showed that all the states except Tamil Nadu registered positive and relatively high growth in yield during the recent times. However, a higher level of inter-district variation in rice productivity was observed in states such as Madhya Pradesh, Bihar and Orissa. Although average paid-out cost increased overtime, a more than proportionate increase in value of output had led to increase in farm business income from paddy cultivation. Except Assam, all other states have shown positive growth in TFP during 1991/2–2012/3. However, except Andhra Pradesh, other states showed no improvement in technical efficiency gains. These results imply that there exists a great potential to improve rice production through adoption of suitable modern varieties, better management practices and institutional mechanism for supply of inputs.

Annexure: Measurement of Total Factor Productivity

Total factor productivity (TFP) is calculated as the ratio of aggregate output to aggregate input. In India, most studies used Tornqvist index for constructing output and input indices by using quantity and price information (Kumar and Mruthynjaya 1992; Evenson et al. 1999; Mukherjee and Yoshimi 2003; Kumar et al. 2004, 2008; Chand et al. 2011). This index has been preferred for its niceties of theoretical properties as established by Diewert (1976, 1978). But, this index is considered to be a descriptive measure of productivity change. Tornqvist index does not allow for decomposition of productivity growth (Färe et al. 1994), and either it requires the knowledge of underlying production technology (Ray 2004, p. 274). Further, TFP growth estimated by using this method is inappropriately interpreted as technical change (Mahadevan 2002). However, distance function-based Malmquist productivity index lends decomposition of productivity growth into technical efficiency change (catch-up) and technical change (innovation) between two time periods. Malmquist productivity index was originally introduced by Caves et al. (1982), and its use in empirical studies was popularised by Färe et al (1994).

Distance function is useful to describe a multi-input, multi-output technology without specifying behavioural objectives of the farmers. To define Malmquist total factor productivity index, the concept of output distance function is used here. The output distance function measures maximal proportional expansion of output vector given input vector. Following Färe et al. (1994), for each time period t = 1, 2,…T, the production technology set S ^t consists of all feasible input vector $x^{t} \in R_{ + }^{N}$ and output vector $y^{t} \in R_{ + }^{M}$ such that x can produce y. The technology set is represented as:

$$S^{t} = \left\{ {\left( {x^{t} ,y^{t} } \right)} \right.{:}\;x^{t} \;{\text{can}}\;{\text{produce}}\;\left. {y^{t} } \right\}$$

The output distance function defined at t is as follows.

$$D_{0} \left( {x^{t} ,y^{t} } \right) = \hbox{min} \left\{ {\theta {:}\;\left( {x^{t} ,y^{t} /\theta } \right) \in S^{t} } \right\}$$

$D_{0} \left( {x^{t} ,y^{t} } \right)$ represents the distance of a farm using x input vector to produce y output vector in period t relative to the reference technology in period t. The distance function $D_{0} \left( {x^{t} ,y^{t} } \right)$ will take a value of less than or equal to one if $\left( {x^{t} ,y^{t} } \right)$ is an element of technology set S ^t. Further, $D_{0} \left( {x^{t} ,y^{t} } \right)$ will take a value of one if $\left( {x^{t} ,y^{t} } \right)$ is located on the boundary of the technology, and it will take a value greater than one if located outside the feasible technology set. Distance function is measured by using Data Envelopment Analysis like linear programming by assuming constant returns to scale (for details see Färe et al. 1994; Coelli 1996; Coelli et al. 1998; Coelli and Prasada Rao 2003).

Under output orientation, Malmquist total factor productivity (TFP) index measures radial distances of observed output between two time periods in relation to a reference technology. Here, Malmquist TFP index measures changes in TFP between two adjacent time periods as the ratio of each output distance relative to a reference technology. Following Färe et al. (1994), Malmquist TFP index between period t and t + 1 can be represented as geometric mean of output oriented indexes: one using technology in period t as a reference technology and another using technology frontier in period t + 1 as the reference. The Malmquist TFP index is written as follows.

$$\begin{aligned} M_{0} \left( {x^{t + 1} ,y^{t + 1} ,x^{t} ,y^{t} } \right) & = \left[ {M_{0}^{t} \left( {x^{t + 1} ,y^{t + 1} ,x^{t} ,y^{t} } \right) \times M_{0}^{t + 1} \left( {x^{t + 1} ,y^{t + 1} ,x^{t} ,y^{t} } \right)} \right]^{1/2} \\ & = \left[ {\frac{{D_{0}^{t} \left( {x^{t + 1} ,y^{t + 1} } \right)}}{{D_{0}^{t} \left( {x^{t} ,y^{t} } \right)}} \times \frac{{D_{0}^{t + 1} \left( {x^{t + 1} ,y^{t + 1} } \right)}}{{D_{0}^{t + 1} \left( {x^{t} ,y^{t} } \right)}}} \right]^{1/2} \\ \end{aligned}$$

The Malmquist productivity index defined in terms of distance functions above evaluates whether the observed input/output combination has improved relative to reference technology in period t and reference technology in period t + 1. The value of productivity index (M ₀) greater than one will indicate a positive TFP growth, less than one the negative TFP growth and equal to one will show the stagnation in TFP growth between the periods t and t + 1. Following Färe et al. (1994), the Malmquist productivity index can be written in the following form.

$$M_{0} \left( {x^{t + 1} ,y^{t + 1} ,x^{t} ,y^{t} } \right) = \frac{{D_{0}^{t + 1} \left( {x^{t + 1} ,y^{t + 1} } \right)}}{{D_{0}^{t} \left( {x^{t} ,y^{t} } \right)}} \times \left[ {\left( {\frac{{D_{0}^{t} \left( {x^{t + 1} ,y^{t + 1} } \right)}}{{D_{0}^{t + 1} \left( {x^{t + 1} ,y^{t + 1} } \right)}}} \right) \times \left( {\frac{{D_{0}^{t} \left( {x^{t} ,y^{t} } \right)}}{{D_{0}^{t + 1} \left( {x^{t} ,y^{t} } \right)}}} \right)} \right]^{1/2}$$

The component outside the square bracket is the ratio of technical efficiency in period t to technical efficiency in period t + 1. This efficiency change component indicates how far the observed production is getting closer or farther from frontier. The expression inside the bracket indicates shift in technology frontier (technical change) between the period t and t + 1. It is measured as the geometric mean of shift in technology between two periods evaluated at input levels x ^t and x ^t+1. The value of efficiency change component greater than one indicates that the production unit is catching up to the frontier in period t + 1 as compared the period t. The improvement in technical change provides evidence of innovation between two periods, and the value of technical change greater than one shows technical progress. In other words, TFP growth can be written as,

$$\begin{array}{*{20}l} {{\text{TFP growth }} = } \hfill & {\text{Technical Efficiency Change}} \hfill & \times \hfill & {\text{Technical Change}} \hfill \\ {} \hfill & {\left( {\text{Catching up effect}} \right)} \hfill & {} \hfill & {\left( {\text{Frontier shift effect}} \right)} \hfill \\ \end{array}$$

Following Färe et al. (1994), technical efficiency change can be decomposed into pure technical efficiency change (estimated under variable returns to scale) and scale efficiency change. This can be specified as,

Technical Efficiency Change = Pure Technical Efficiency Change × Scale Efficiency Change.