Geoscience Reference
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productivity across time, that is, sigma (σ) has been examined.
An approach to observe the occurrence of sigma (σ) conver-
gence is to plot the evolution of standard deviations over time.
For example, McErlean and Wu (2003) show the evolution of
σ-convergence by plotting the standard deviations of productiv-
ity across the three geographic regions of China from 1985 to
2000. It occurs when the dispersion of rice productivity across
73 districts of India tends to decrease over time.
That is, if
σit + T < σit
(11.1)
where σit is the dispersion of rice yield (yit) across districts i
at the initial period and σit + T is the dispersion of rice yield
across districts at subsequent periods.
11.7
Results and discussions
I analyse the σ-convergence by examining changes in the evo-
lution of the coefficient of variation (CV) over time at aggre-
gate (national) and disaggregate scales (ecological regions).
Analysis of the evolution of σ-convergence across the different
scales is especially informative to see whether the pattern of
σ-convergence observed at the aggregate scale is also found
within the disaggregate scale (e.g. ecological regions). The
analysis of σ-convergence provides a measure of variability of
rice productivity. It occurs when the variability of rice produc-
tivity across the districts decreases over time. Conversely, the
increase of variability implies in σ-divergence.
In general, there have been no distinct patterns to suggest
the occurrence of σ-convergence in rice productivity because
the CVs have not reduced substantially across the districts of
India during the 12 years. The CV in 1991/1992 was about 32%
and continued to decline until 1996/1997, with a record low in
1995/1996 (23%). The trend reversed thereafter, reaching an all-
time high of 40% in 2002/2003. The finding at the aggregate
level does not preclude the fact that σ-convergence may not have
occurred within a specific ecological region. In the next section,
I analyse the evolution of CVs at the scale of ecological regions
to see if the pattern observed at the national (coarse-scale) level
is also found within the ecological (finer-scale) regions.
Figure 11.2 presents the general trends of the evolution of
CVs over time in the three ecological regions. Although exhib-
iting fluctuations, the CVs have declined in 20 districts of the
