individualization in the transition from centrally planned economies (Tanaka 2007). Alternatively, they may be chosen by producers who trade off benefits against costs of fragmentation. A key benefit is the ability to diversify the plot portfolio to include plots with different attributes (cropland, pastures, orchards, vineyards) so as to reduce exposure to price risk or variability of production due to flood, drought, or pests (McCloskey 1975) or ease bottlenecks and smooth out seasonal variability in labor demands (Fenoaltea 1976). Costs accrue because fragmented plot holdings may preclude use of machinery and, depending on the location of plots, may require spending more time to move between plots (Bentley 1987). Ascertaining the impact of fragmentation will thus require proxies for associated costs as well as benefits.

Studies that include only the number of plots cultivated or the Simpson index of land fragmentation that ranges from zero to one, with higher values corresponding to higher fragmentation but fail to account for risk-reduction benefits, often find negative effects of fragmentation. In 5 Chinese provinces (Jilin, Shandong, Jiangxi, Sichuan, Guangdong), a production function for a sample of some 1,000 farmers with 5 key corps (maize, early and late rice, wheat, and tubers) in 1994 suggests a significant negative impact: exogenous addition of one plot is estimated to reduce output by 2 to 10 percentage points depending on the crop (Wan and Cheng 2001).<sup>1</sup> In Bangladesh, for a small sample of 298 farm households with an average of 4.4 parcels per holding in 2000, a frontier production points towards a negative productivity- and efficiency-effects from plot fragmentation (Rahman and Rahman 2008). Estimating a yield function on a small panel from North Vietnam for 200 farmers on very fragmented holdings (mean and median plot numbers of 6.84 and 6 and Simpson index of 0.59 and 0.68, respectively) in 2000/1 similarly suggests that number of plots has a statistically negative effect on yield and increased family labor use and other money expenses (Hung _et al._ 2007). On the other hand, a small sample (227 households) from Hubei province in China finds that the number of plots had no significant effect on crop production (as measured by a production function). Moreover, a program to reduce land fragmentation did not achieve its main goal, possibly because with relatively abundant labor, the scope to use any labor savings in other tasks was limited and low levels of technology implied significant fragmentation-related benefits in terms of risk-reduction (Wu _et al._ 2005).<sup>2</sup> One way of accounting for potential benefits from fragmentation more explicitly is to explore impacts on variability of output in a panel setting. Kawasaki (2010) applied this approach together with a cost stochastic frontier function on a large panel of Japanese rice farmers (18,000 farms per year from 1995-2006 rice production cost statistics) who cultivate a mean of 4 parcels with a Simpson index of 0.8 together with a

> 1 The magnitude of these effects is used to argue that efforts to eliminate fragmentation, either by improving functioning of factor markets or by programs aimed specifically at land consolidation, would be worthwhile (Chen _et al._ 2009).

> 2 This mirrors evidence from Albania where fragmentation does not seem to negatively affect output and crop abandonment due to ill-functioning land market institutions, in particular the registry seems to be a more potent factor in reducing land use efficiency (Deininger _et al._ 2012).

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