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''The Index Number Problem: A Differential Geometric Approach'', a Ph.D. Thesis in Economics at Harvard by Pia Malaney, offers a groundbreaking analysis of index number theory using differential geometry, addressing long-standing inconsistencies in traditional economic indices. The thesis introduces the concept of an economic derivative, resolving discrepancies between indices like Paasche and Laspeyres by developing a unique differential geometric index equivalent to the Divisia index. This approach not only provides a consistent and accurate measure of economic changes but also offers practical applications in welfare analysis, challenging the traditional reliance on the Konus index. | ''The Index Number Problem: A Differential Geometric Approach'', a Ph.D. Thesis in Economics at Harvard by Pia Malaney, with contributions by Eric Weinstein, offers a groundbreaking analysis of index number theory using differential geometry, addressing long-standing inconsistencies in traditional economic indices. The thesis introduces the concept of an economic derivative, resolving discrepancies between indices like Paasche and Laspeyres by developing a unique differential geometric index equivalent to the Divisia index. This approach not only provides a consistent and accurate measure of economic changes but also offers practical applications in welfare analysis, challenging the traditional reliance on the Konus index. | ||
In addition to resolving the index number problem, the thesis explores the welfare implications of using Divisia indices, particularly in relation to changing consumer preferences and psychological neutrality. Malaney further extends the analysis to household migration decisions under uncertainty, demonstrating how traditional models oversimplify the decision-making process by neglecting risk aversion and household-level dynamics. The work concludes by advocating for a more comprehensive understanding of economic indices and migration policies, highlighting the need for refined economic metrics and more nuanced policy approaches. | In addition to resolving the index number problem, the thesis explores the welfare implications of using Divisia indices, particularly in relation to changing consumer preferences and psychological neutrality. Malaney further extends the analysis to household migration decisions under uncertainty, demonstrating how traditional models oversimplify the decision-making process by neglecting risk aversion and household-level dynamics. The work concludes by advocating for a more comprehensive understanding of economic indices and migration policies, highlighting the need for refined economic metrics and more nuanced policy approaches. | ||