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Causal Effects in Matching Mechanisms with Strategically Reported Preferences

Marinho Bertanha, Margaux Luflade, Ismael Mourifié

Abstract

A growing number of authorities use mechanisms to allocate students to schools in a way that reflects student preferences and school priorities. However, most real-world mechanisms incentivize students to strategically misreport their preferences. Misreporting complicates the identification of causal parameters that depend on true preferences, which are necessary inputs for a broad class of counterfactual analyses. We provide an identification approach robust to misreporting and derive sharp bounds on causal effects of school assignment. Our approach applies to allocation rules characterized by placement scores and cutoffs. We use data from a deferred acceptance mechanism that assigns students to university programs in Chile. Matching theory predicts and empirical evidence shows that students behave strategically in Chile because they face constraints on preference submission and have good prior information about school accessibility. Our bounds are informative enough to reveal significant heterogeneity in graduation success with respect to preferences and school assignment.

Causal Effects in Matching Mechanisms with Strategically Reported Preferences

Abstract

A growing number of authorities use mechanisms to allocate students to schools in a way that reflects student preferences and school priorities. However, most real-world mechanisms incentivize students to strategically misreport their preferences. Misreporting complicates the identification of causal parameters that depend on true preferences, which are necessary inputs for a broad class of counterfactual analyses. We provide an identification approach robust to misreporting and derive sharp bounds on causal effects of school assignment. Our approach applies to allocation rules characterized by placement scores and cutoffs. We use data from a deferred acceptance mechanism that assigns students to university programs in Chile. Matching theory predicts and empirical evidence shows that students behave strategically in Chile because they face constraints on preference submission and have good prior information about school accessibility. Our bounds are informative enough to reveal significant heterogeneity in graduation success with respect to preferences and school assignment.
Paper Structure (36 sections, 10 theorems, 67 equations, 6 figures, 7 tables)

This paper contains 36 sections, 10 theorems, 67 equations, 6 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Model
  3. Identification with Truthful Reports
  4. Identification with Strategic Reports
  5. Partial Identification of Local Preferences
  6. Partial Identification of Causal Effects
  7. Assignment to College Programs and Graduation in Chile
  8. Institutional Setting and Evidence of Strategic Behavior
  9. Centralized college application system in Chile.
  10. Strategic behavior.
  11. Results
  12. Average Structural Functions and the Importance of Preferences for Graduation Outcomes
  13. Setup.
  14. On the importance of preferences for graduation outcomes.
  15. Role of behavioral assumptions.
  16. ...and 21 more sections

Key Result

Lemma 1

Suppose Assumption aspt:continuity holds. Consider a school $j$ with cutoff $c_j$ in the interior of the support $\mathcal{S}_j$ , and choose two schools $k ,{}{}{} , l \in \mathcal{J}^0$ such that $\mathbb{P}[Q_j=(k ,{}{}{} , l)|S_j=c_j]>0$. Then , for any function $g \in \mathcal{G}

Figures (6)

  • Figure 1: Cutoffs of Selective Programs
  • Figure 2: Applications to a program peak among applicants with scores close to the cutoff
  • Figure 3: Evidence of strategic behavior of the discontinuous type
  • Figure 4: Graduation Rates if Assigned to Bachillerato de Ingreso Comun at UChile
  • Figure 5: Effects of assignment to Medicine at PUC vs. next-best alternatives
  • ...and 1 more figures

Theorems & Definitions (25)

  • Definition 1: Stability
  • Definition 2: Cutoff Characterization
  • Definition 3: Counterfactual Budget Sets
  • Example : SD Example , Part I
  • Definition 4: Local Preferences
  • Example : SD Example , Part II
  • Definition 5: Comparable Pairs
  • Lemma 1
  • Proposition 1
  • Definition 6
  • ...and 15 more