The MSII is based on the estimated slope parameter by fitting a linear regression model that considers the MMR as the dependent variable and the Ridit (the cumulative relative position of each province with respect to the socioeconomic indicator, which ranges between 0 and 1) as the independent variable.
The MSII was computed as MSII = b ([Ridit.sub.Min] - [Ridit.sub.Max]), where b is the estimated slope parameter computed by fitting the linear regression model.
The 95% CI for the MSII was computed as [[b.sub.U] ([Ridit.sub.Min] - [Ridit.sub.Max]), [b.sub.L] ([Ridit.sub.Min] - [Ridit.sub.Max])], where [b.sub.L] and [b.sub.U] are, respectively, the lower and upper limits computed from the 95% CI for the slope parameter.
Of the five socioeconomic indicators that were statistically associated with MMR, only three proved to have statistically significant MMR inequality measures when using the MSII and PRSII: total fertility rate, GDP, and the percentage of households with electricity (Table 3).
With respect to the total fertility rate for each province, the MSII value of 26.1 (Table 3) indicates that there are 26.1 more maternal deaths per 100 000 live births in the province with the highest total fertility rate (the most disadvantaged).
Considering the values for each province in Ecuador, the MSII value of 28.8 (Table 3) indicates that there are approximately 32 additional maternal deaths per 100 000 live births occurring in the province with the lowest GDP than in the province with the highest GDP.
For [lambda][e.sub.s][[??].sub.2][[bar.p].sub.es2] [greater than or equal to] [DELTA][k.sup.*.sub.s2], we get the optimal auction reserve price of supplier with MSII
[[bar.p].sup.*.sub.es2] = ([bk.sub.s][k.sub.m](1 + [e.sub.m]/[e.sub.s])/([4k.sub.m] - [bz.sup.2.sub.m])[[??].sup.2.sub.2])[p.sub.e]; among it [[??].sub.2] = [bk.sub.s]([phi] - bc)/(4[bk.sub.s] - 2[([beta] + [bz.sub.s]).sup.2] - [kb.sup.2][z.sup.2.sub.m]) is the initial production in MSII with loose carbon policy ([lambda] = 0).
For [lambda][e.sub.m][[??].sub.2][bar.p].sub.em2] [greater than or equal to] [DELTA][k.sup.*.sub.m2], we get the optimal auction reserve price of manufacturer in MSII:
Similarly, in the context of MSII, we can get the optimal increase in carbon price with tariff [lambda]:
where [A.sub.2] = 2[[??].sub.2][[2e.sub.s]([beta] + [bz.sub.s]) + [bar.k][be.sub.m][z.sub.m]] -[lambda][[e.sub.0] [beta] + [bz.sub.s]) + [be.sub.s][z.sub.0]] + [e.sub.s]([phi] - bc) and [[??].sub.2] = ([beta] + [bz.sub.s])([phi] - bc)/(4[bk.sub.s] - 2[([beta] + [bz.sub.s]).sup.2] [[bar.k]b.sup.2][z.sup.2.sub.m]) is the initial reduction rate per unit raw material in MSII. [psi]([DELTA][p.sup.*.sub.e2], [lambda]) is the government's optimal mixed carbon policy.
Interestingly, the top five countries that score poorly in the MSII
are also those that have witnessed a marked increase of support for non-mainstream parties in recent years, boosting political fragmentation.