Search

We propose a new algebraic approach to graph transformation, called the Pullback-Pushout ( pbpo ) approach, where we combine smoothly the classical modifications to a host graph specified by a first part of a rule, defined as a span of graph morphisms, with the cloning of structures specified by a second span. The motivation behind this new approach is to support cloning of structures in an elegant and efficient way. After a formal definition of the proposed approach, we demonstrate that pbpo rewriting is a conservative extension of agree and the Sesqui-Pushout approaches. Contrary to agree , we show that the proposed pbpo transformation can easily be extended to cope with attributed graphs. In general, totally attributed graphs are not closed under pbpo transformation. We propose sufficient conditions which guarantee that the attribution of transformed graphs is total. Furthermore, a pbpo transformation can affect all parts of a host graph including non local parts (i.e., parts which are outside the image of the left-hand side of a rule). We propose and discuss some conditions which ensure a form of locality of pbpo transformations.

In this paper, we utilize decomposition methods to document the extent and drivers of the performance gap in Malawi between firms with a female owner and firms with a male owner. We find that, on average, male-owned businesses in Malawi earn profits more than double (120%) those of female-owned businesses. We use Kitagawa-Oaxaca-Blinder (KOB) mean-decomposition techniques and recentered influence function (RIF) regressions applied along the earnings distribution, coupled with data from a novel multi-topic household survey rich in details about entrepreneurship, to identify what proportion of the gender gap in business profits can be attributed to: (i) differences in average characteristics of profit-generating factors (composition effect) and (ii) gender differences in the returns to these factors (structure effect). We find that 59.8% of the mean gender gap is explained by gender differences in the levels of observable attributes, with the remaining 40.2% attributable to the lower returns to observable attributes obtained by female owners, i.e., female structural disadvantage. The composition effect is primarily driven by female owners’ role as the primary caregiver in most households and a lack of capital. The female structural disadvantage can largely be attributed to female owners’ heightened perception of sexual hostility in the work environment and non-cognitive skills related to entrepreneurship (perseverance in challenging tasks and environments, optimism, and passion for work). When looking along the distribution, capital stock appears to be a primary driver of the composition effect except in the bottom quintile of firms. In contrast, caregiving responsibilities are a driver of the composition effect in the bottom three quintiles only. Differences in the returns to capital appear to be a very significant driver of the female structural disadvantage in the bottom quintile.