The pattern of tenure suggests that land fragmentation is exogenous to the house- hold. A key part of the literature is how to measure it. Land fragmentation is the dispersion of parcels across the landscape, as illustrated in Figure 4.2, where we see examples of consolidated and fragmented parcels. There are multiple approaches to measure land fragmentation, summarized in Table 4.3.
The simplest measure of land fragmentation is the number of parcels K held by a household. All else being equal, more parcels suggests greater fragmentation. However this does not take into account the different size of parcels, which we denote αk. One measure incorporating both parcel count and size is the Simpson FI measure:
Simpson land fragmentation index (FI):
F I = 1 − PK k α 2 k (PK k αk)2 (4.2)
3. Fragmentation decreases as the area of large parcels increases and that of the small parcels decreases.
The Januszewski index is similar to the Simpson index in scale and compos- ition (Januszewski, 1968).4 For conciseness we do not report it in our principal regressions.
We also consider a measure of fragmentation which captures the variability of fragment size, as proposed by Monchuk et al . They point out that the Simpson index conflates the effect of increased number of parcels δF I
δn > 0 with the effect of increased variability in fragment areas δF Iδσ2 < 0. Since both of these can be
thought to increase’ fragmentation, they propose to isolate the effect of variability in fragment area through the following measure:
Sk=
p(αk− ¯α)2 ¯
α (4.3)
A shortcoming of the above is that it registers a value of 0 for a single parcel aswell as for a number of parcels with the same size. It should therefore be considered as complementary to other measures, such as the number of parcels, rather than a perfect substitute. For a household we take the weighted average of Sk.
The above measures consider the size and number of parcels, but not their physical dispersion. If the correlation between fragmentation and labor costs is driven by travel time, this is an important measure. With the georeferenced co- ordinates of each parcel, we calculate Dt, the minimum round trip distance to reach all parcels and return home (Igozurike, 1974).
4J = 1 − (√PKk αk
Pn
K√αk), As K → 1 fragmentation increases.
Dt= min xkj K X k K X j6=k ckjxkj (4.4) where xkj =
1 use path between parcel k and j
0 otherwise
and ckj is the distance from plot k to plot j. We calculate Dt using a travelling salesman algorithm, finding the shortest route connecting multiple parcel locations as defined by their longitude and latitude.5
Parcel Characteristics
Calculating the Simpson Fragmentation Index and deviations in parcel size both require an accurate measures of parcel area α. Most measures in the data were calculated using GPS coordinates. When GPS observations were missing, enu- merators measured area using a rope-and-compass method. They also inquired as to the farmer’s own estimate of the field size. Across three rounds 10.4% of parcels were missing area measurements taken by GPS, the bulk of them in the first round. Where GPS measures were missing but rope-and-compass measures were available, we used the rope-and-compass measures of α. This allowed us to recover half of the missing observations. In order to validate this substitution,
We attempted to incorporate the self-reported measures, but many of these were expressed using traditional Ethiopian measures of area, such as the ’timad’.7 Our attempts to convert these measures to standard hectares found them to be poorly correlated with GPS measures of area.8 Furthermore, it is well documented that self-reported measures of parcel area suffer from non-random measurement error (Carletto et al., 2015).
The number of parcels K, their average size ¯α and the total area farmed by a household P αk are reported in Table 4.4a. We find evidence that the pattern of land tenure due to land redistribution persists. In the highland regions most affected by the reforms, the number of parcels are in the range of ≈ (3.5, 4.5), which corresponds neatly with the four categories of land discussed earlier. In other parts of the country, the number of parcels is closer to 2. In these regions land tenancy is characterized by homesteads. The size of parcels varies, but tends towards a quarter or half hectare. Recall that the distribution was done in ‘timads’, approximately a quarter hectare. Finally, the total number of hectares held by households is between .9 and 1.5 hectare, reflecting strict limits on large land tenure and further evidence of the legacy of land redistribution efforts.
In addition to area α, the data-set contains geovariables matched at the plot level using non-scrambled GPS coordinates. These include:
1. Distance from plot to household (in km)
2. Slope of the plot (in percentages)
7A ‘Timad’ is traditionally the amount of land that can be plowed in a day.
8The LSMS Ethiopia documented district specific units of conversion from ‘Timad’ to hectare.
We therefore attempted to convert these self-reported measures but produced a large number of outliers. As an alternative, we tried using a standard conversion for the ‘Timad’, treating it as 1/4 of an acre in line with the FAO standard. However, comparisons between self-reported area and GPS measurements when the two overlapped showed the former to be inconsistent. See appendix for further details.
3. Plot elevation (in metres)
4. Plot potential wetness index9
These plot level characteristics were averaged at the parcel level, weighted by plot area. They are summarized in Table 4.4b.