The Simple Structure of Top Trading Cycles in School Choice

2017 ◽  
Author(s):  
Jacob D. Leshno ◽  
Irene Lo
Keyword(s):  
School Choice ◽  
Simple Structure ◽  
Top Trading Cycles

scholarly journals THE EQUITABLE TOP TRADING CYCLES MECHANISM FOR SCHOOL CHOICE

2018 ◽  
Vol 59 (4) ◽  
pp. 2219-2258 ◽  
Author(s):  
Rustamdjan Hakimov ◽  
Onur Kesten
Keyword(s):  
School Choice ◽  
Top Trading Cycles

The Cutoff Structure of Top Trading Cycles in School Choice

2020 ◽  
Author(s):  
Jacob D Leshno ◽  
Irene Lo
Keyword(s):  
School Choice ◽  
School Quality ◽  
Competitive Equilibrium ◽  
Optimal Investment ◽  
Comparative Statics ◽  
Closed Form Solutions ◽  
Top Trading Cycles ◽  
Deferred Acceptance

Abstract This paper develops a tractable theoretical framework for the Top Trading Cycles (TTC) mechanism for school choice that allows quantifying welfare and optimizing policy decisions. We compute welfare for TTC and Deferred Acceptance (DA) under different priority structures, and find that the choice of priorities can have larger welfare implications than the choice of mechanism. We solve for the welfare-maximizing distributions of school quality for parametrized economies, and find that optimal investment decisions can be very different under TTC and DA. Our framework relies on a novel characterization of the TTC assignment in terms of a cutoff for each pair of schools. These cutoffs parallel prices in competitive equilibrium, with students’ priorities serving the role of endowments. We show that these cutoffs can be computed directly from the distribution of preferences and priorities in a continuum model, and derive closed-form solutions and comparative statics for parameterized settings. The TTC cutoffs clarify the role of priorities in determining the TTC assignment, but also demonstrate that TTC is more complicated than DA.

A Comparison of Simple Structure Rotation Criteria in Temporal Exploratory Factor Analysis for Event-Related Potential Data

Methodology ◽  
2019 ◽  
Vol 15 (Supplement 1) ◽  
pp. 43-60 ◽  
Author(s):  
Florian Scharf ◽  
Steffen Nestler
Keyword(s):  
Factor Analysis ◽  
Exploratory Factor Analysis ◽  
Simple Structure ◽  
Ground Truth ◽  
Event Related Potential ◽  
Suitable Alternative ◽  
Factor Rotation ◽  
Rotation Methods ◽  
Simple Structure Rotation ◽  
Temporal Overlap

Abstract. It is challenging to apply exploratory factor analysis (EFA) to event-related potential (ERP) data because such data are characterized by substantial temporal overlap (i.e., large cross-loadings) between the factors, and, because researchers are typically interested in the results of subsequent analyses (e.g., experimental condition effects on the level of the factor scores). In this context, relatively small deviations in the estimated factor solution from the unknown ground truth may result in substantially biased estimates of condition effects (rotation bias). Thus, in order to apply EFA to ERP data researchers need rotation methods that are able to both recover perfect simple structure where it exists and to tolerate substantial cross-loadings between the factors where appropriate. We had two aims in the present paper. First, to extend previous research, we wanted to better understand the behavior of the rotation bias for typical ERP data. To this end, we compared the performance of a variety of factor rotation methods under conditions of varying amounts of temporal overlap between the factors. Second, we wanted to investigate whether the recently proposed component loss rotation is better able to decrease the bias than traditional simple structure rotation. The results showed that no single rotation method was generally superior across all conditions. Component loss rotation showed the best all-round performance across the investigated conditions. We conclude that Component loss rotation is a suitable alternative to simple structure rotation. We discuss this result in the light of recently proposed sparse factor analysis approaches.

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