The effect of land fragmentation on the productivity and technical efficiency of smallholder maize farms in Southern Rwanda

3.0 METHODS AND PROCEDURES

3.1 Theoretical model

3.1.1 Indicators of land fragmentation

Different researchers have used several measurement units in their attempt to measure land fragmentation. Common measures include the Simpson index (SI), the Januszewski index (JI) and average farm size.

The Simpson Index ( Blarel Benoit,  Peter Hazell,  Frank Place and  John Quiggin, 1992), which is defined as:

Where n is the number of plots, and is the area of each plot. This index is located within the range of 0 to 1. A higher SI value corresponds with a higher degree of land fragmentation. The value of the Simpson index is determined by the number of plots, average plot size and the plot size distribution. It also does not take farm size, distance and plot shape into account.

Average farm size (Nguyen et al. 1996) defined as:

Where S is the size of the farm and N is the number of plots. When N is large, average plot size, P is small. This implies that as fragmentation increases, average farm size reduces and vice-versa. This measure of land fragmentation simply looks at the way in which a farm is subdivided into a given number of plots. The drawback of using average farm size as a measure of land fragmentation is that it only considers subdivision of the same piece of land (farm) due to inheritance only.

The Januszewski index (Raghbendra et al. 2005) defined as:

Where n is the number of plots, and is the area of each plot. This index is located within the range of 0 to 1. The smaller the JI value the higher degree of land fragmentation. The JI value combines information on the number of plots, average plot size and the size distribution of the plots. It has three properties: fragmentation increases (the value of the index decreases) when the number of plots increases, fragmentation increases when the average plot size declines, and fragmentation decreases when the inequality in plot sizes increases. The index, however, fails to account for farm size, plot distance, and shape of plots.

Single-dimension indicators of land fragmentation (Shuhao, 2005): There are three indicators/measures of land fragmentation; (1) plot size, (2) number of plots per household and, (3) the distance from household residences to plots. This study used these three measures of land fragmentation because we wanted to capture explicit effects of each single-dimension indicator on the productivity and technical efficiency of farms.

3.1.2 Measuring technical efficiency

Choosing between a parametric (stochastic frontier model) and a non-parametric (Data Envelopment Analysis) approach to measure efficiency has been controversial. Each has its strengths and weaknesses (Coelli and Perelman, 1999). The parametric analysis deals with stochastic noise, and allows hypothesis testing on production structure and efficiency. However, this method has to specify a functional form for the production frontier and imposes a distributional assumption on the efficiency term. The non-parametric method does not impose such restrictions, but it assumes the absence of measurement or sampling error. The choice between these approaches, therefore, depends upon the objective of the research, the type of farms that are analyzed, and data availability.

The stochastic frontier method has been used for both cross-sectional and panel data. In Tanzania, Mbelle and Sterner, (1991) applied the model to analyze the importance of foreign exchange in industries. Other studies include among others, those of Battese and Coelli (1995); Raghbendra et al (2005); Hyuha et al. (2008) and Bagamba (2007).

This study used the stochastic frontier approach - a parametric method - to analyze the effect of land fragmentation on the technical efficiency of smallholder maize farms in Southern Rwanda. The main reason for this choice is that maize production in Rwanda is subject to weather disturbances and heterogeneous environmental factors like soil quality. Moreover, the respondents might not always answer all the questions precisely, due to for example having varied perceptions, and this will affect measured efficiency (Chen et al., 2003).