1. To study the trend of area, production and productivity of sugarcane in South Gujarat region
2. To examine the total factor productivity growth and its sources in the sugar mills of South Gujarat region
3. To identify the constraints faced by sugar mills of South Gujarat region
4. To suggest the measures to improve the productivity of sugar mills of South Gujarat region

Sugarcane is intensively grown in the Gujarat, in which South Gujarat region alone accounts for about 90 per cent of total area under the crop  and  also  contributes  near  about 92 per  cent  of  its  total production  in  the  state. Out of total production of sugar, Gujarat state contribution about 5 % of total sugar production of India. In Gujarat, there are 19 Sugar co-operative factories. Out of this 16 Sugar co-operative factories are in South Gujarat region. Therefore, the region will be purposively selected for the study. The performance of sugarcane crop in the state of Gujarat in respect of area, production and productivity will be studied. The secondary data of area, production and productivity will be collected for the period from 2000-01 to 2019-20 year from book published by Office of Directorate of Agriculture, Gujarat state, Gandhinagar. The data related to Sugar co-operative factories will be collected from present working Sugar factories of South Gujarat (India) for the period 2011-12 to 2019-20. These Sugar co-operative factories are diverse in size, origin, ownership and presumed abilities. However, all these Sugar co-operative factories are in the same line of business (i.e., sugar production) and are working under similar market conditions. The TFP growth is estimated through slack based measure (SBM) -DEA based Malmquist Productivity Index (MPI) model using one output variables, viz., sugar production (measured in million quintals) and six input variables, namely, installed capacity (as proxy for fixed capital) measured in sugar cane crushed per day in tones (TCD),  actual sugar cane crushed per day in tones (TCD), crushing days (no. of days in a year), actual crushing days (no. of days in a year), raw material (sugarcane) measured in million quintals and energy & fuel measured in million rupees. As far as the details of the sugar at the state level are concerned Directorate of Sugar, Gujarat State, Gujarat Rajya Sahakari Khand Udyog Sangh, Ahmedabad.

Compound Growth Rate

For Gujarat state as a whole compound growth rate for area, production and productivity of sugarcane crop will be calculated. The index numbers of area, production and productivity of sugarcane crop will be calculated by taking agricultural year 2000-01 as the base year. The compound growth rates will be calculated by fitting the exponential function to the index number of the area, production and productivity. The following form of the exponential function will be used:

Y = abt

Where,

Y = dependent variable for which growth rate is to be estimated

a = constant/intercept

b = regression coefficient

t = time variable in year

The compound growth rate will be obtained using logarithmic form of the equation as below:

Log Yt = Log a +  t Log b

Then the per cent compound growth rates (g) will be computed by using the relationship:

g = (antilog of log b – 1) *100

where,

g = compound growth rate per annum in percent 

Productivity Measurement Approaches

A non-parametric approach, known as Malmquist Productivity Index (MPI) will be applied on the panel data of 9 years collected from 19 sugar mills of the state. Non-oriented and non-radial slack based measure (SBM) - DEA method will used for estimation of the TFP growth and its decomposition into technical efficiency change and technical progress.

Most commonly used measures of productivity are partial or single factor productivity (SFP) and total factor productivity (TFP). SFP is the ratio of total output to the quantity or number of the factor for which productivity is to be estimated. SFP provides a distorted view about the contribution of a factor to the total production. For instance, partial productivity of labour can be increased by reducing quantity of labour and increasing quantity of capital in the production unit.

Therefore, concept of TFP is more relevant in context of resource use efficiency. TFP is defined as the ratio of weighted sum of output to the weighted sum of inputs. Over the last three decades, researchers have developed several theories and methods of TFP measurement. Before the mid-1990s, most studies estimated TFP growth by growth accounting approach (Hsiao and Park, 2002). This approach is based on unrealistic assumptions of perfect competition and constant returns to scale. It assumes that a firm operates on its production frontier, implying that it has 100 per cent technical efficiency. Thus, TFP growth measured through this approach is due to technical change, not due to technical efficiency change (Mawson et al., 2003). In recent years, stochastic frontier analysis and DEA-based MPI have become popular approaches that use panel data for estimation of TFP of individual decision making units (DMUs). These approaches do not assume that all production units operate at 100 per cent technical efficiency.

According to the MPI approach, TFP can increase not only due to technical progress (shifting of frontier) but also due to improvement in technical efficiency (catch-up). This approach has become quite popular because: (i) it does not require price data, therefore suitable when price data are not available or price data are distorted; (ii) it rests on much weaker behavioural assumptions, since it does not assume cost minimizing or revenue maximizing behaviour; (iii) it uses panel data and provides a decomposition of productivity change into two components—technical change and technical efficiency change. The significance of the decomposition is that it provides information on the source of overall productivity change. MPI is DEA-based approach but unlike DEA that is static in nature as it assesses the efficiency of a DMU in relation to the best practice DMUs in a given year, MPI also accounts for the shift of frontier overtime. Since it is capable of decomposing the productivity growth into technical efficiency change and technical progress, it is able to shed light on the mechanism of productivity change (Ma, et al., 2002). The DEA based MPI approach was initially introduced by Caves, Christensen and Diewert (CCD) in 1982 and was empirically applied by Fare, Grosskopf, Lindgren and Roos (FGLR) in 1992 and Fare, Grosskopf, Norris and Zhing (FGNZ) in 1994. Since then, several extended versions of MPI have been developed. A few of them are: Ray and Desli (1997), Balk (2001), Kumar and Russell (2002), Chen (2003), Chen and Ali (2004), Tone (2004) and Sharp et al. (2005).

Efficiency estimated through the conventional DEA models (CCR and BCC models) is a radial measure and does not directly take into account the input-output slacks. In order to overcome this problem, recently researchers have proposed several extended versions of basic DEA models. Tone has developed a slacks-based measure of efficiency (Tone, 2001) and super efficiency (Tone, 2002). These models are non-radial and deal with input and output slacks directly. The radial MPI approach cannot precisely estimate the TFP growth as it does not account for input and output slacks. To overcome this deficiency, MPI can be estimated using slacks-based non-radial DEA models. Non-radial MPI can be computed using input or output orientation. Input-oriented SBM models take input slacks into account but do not consider output slacks while output oriented SBM models take all output slacks but no input slacks. The non-radial and non-oriented SBM models take care of both the slacks. Therefore we will applied non-radial and non-oriented SBM-DEA approach as proposed by Tone (2004) to compute MPI and its components—TECHCH and EFFCH. This approach appears to be superior to the traditional one because: it directly deals with the input and output slacks; it is unit invariant; and the efficiency estimated by it is reference-set dependent (Tone, 2004).

The SBM-DEA Models

As stated above, radial MPI model does not take into account the input/output slacks. To overcome this shortcoming, MPI will be computed using ‘Slack-based Nonradial and Non-oriented’ DEA models. The SBM-DEA and super-SBMDEA models as proposed by Tone (2004) to calculate the distance functions. These models are given as: