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Abstract
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Before
In countries with centralized admission systems, some applicants have access to outside options, also known in the literature as off-platform or out-of-system options. These outside options may include private educational institutions, study abroad programs, online education, and the opportunity to postpone education to explore alternative activities.
The presence of outside options for some applicants has been shown to result in inefficient allocations and reduced welfare for applicants, due to centralized offers being rejected by some applicants in favor of outside options and the subsequent reallocation of vacant places in the aftermarket being hampered by frictions (Kapor et al. (2024)). Additionally, the presence of outside options could reduce the efficiency and welfare of some applicants due to the distortions it may introduce in their decisions within the centralized system.
This study aims to analyze how the presence of outside options for some applicants affects the decisions of all applicants in a centralized admission system under the deferred acceptance (DA) mechanism. I consider two cases: 1) when the length of the ranked ordered list (ROL) of educational programs that applicants can submit is unconstrained, and 2) the case of constrained ROLs. For each of these cases, I also examine whether embedding the outside option into the centralized admissions system affects the decisions of applicants, as well as the characteristics of the resulting matchings.
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After
In countries with centralized admission systems, some applicants have access to outside options. This study aims to analyze how the presence of outside options for some applicants affects the decisions of all applicants in a centralized admission system under the deferred acceptance (DA) mechanism. I consider two cases: 1) when the length of the ranked ordered list (ROL) of educational programs that applicants can submit is unconstrained, and 2) the case of constrained ROLs. For each of these cases, I also examine whether integrating the outside option into the centralized admissions system affects the decisions of applicants, as well as the characteristics of the resulting matchings.
Preliminary results are as follows. I find that, consistent with theoretical predictions, when the length of ROLs is constrained and the outside option is not integrated into the admissions system, participants without access to the outside option adopt a more cautious application strategy compared to those with such access, and are less inclined to truthfully list their top-ranked choice. However, contrary to theory, the incorporation of outside options into the system significantly alters the strategies and matching outcomes of the participants, even if the aftermarket is frictionless when the outside option is not integrated.
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JEL Code(s)
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Before
I21, I28
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After
D47, I21, I24, I28
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Last Published
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Before
October 07, 2024 07:03 PM
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After
January 07, 2025 02:37 AM
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Primary Outcomes (End Points)
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Before
Unconstrained ROLs:
1) Fraction of rounds in which participants report truthful and complete ROLs
Constrained ROLs:
2) Fraction of rounds in which participants submit partially truthful ROLs of the maximum allowed length
3) Fractions of each type of partially truthful ROL of the maximum allowed length
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After
Unconstrained and constrained ROLs:
1) Proportion of participants who truthfully reported their preferences in all 12 of their submitted ROLs
2) Average share of truthful ROLs submitted by participants
3) Average share of ROLs with the top prize type A as first priority (out of 12)
Constrained ROLs only:
4) Average share of ROLs with top prize type A (out of 12): lack of A in ROL indicates more cautious strategy
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Primary Outcomes (Explanation)
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Before
Unconstrained ROLs:
1) Fraction of rounds in which participants report truthful and complete ROLs
Hypothesis: The fraction of rounds in which participants report their true preferences over prizes, listing all prizes, is 1 for all participants, and this does not depend on whether the participant or their competitors have access to the outside options, regardless of whether the outside option is integrated into the centralized system.
Constrained ROLs:
2) Fraction of rounds in which participants submit partially truthful ROLs of the maximum allowed length
Hypothesis: The fraction of rounds in which participants submit partially true ROLs (with no preference reversals) of the maximum allowed length is 1 for all participants, regardless of whether they or their competitors have access to the outside option, and regardless of whether the outside option is integrated into the centralized prize distribution system.
In experimental groups where the outside option is integrated into the centralized system, participants who are highly likely to have access to the outside option will truthfully list it in all their submitted ROLs.
3)Fractions of each type of partially truthful ROL of the maximum allowed length
Explanation: The theoretical model predicts that the fractions of each type of partially true ROL of the maximum allowed length will vary between the control and various treatment groups for participants without access to the outside option. These participants should recognize that the competition for programs less attractive than the outside option is relatively lower, as those with access to the outside option will not be competing for them.
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After
The primary outcomes are used to test the following hypotheses.
Unconstrained ROLs:
Hypothesis 1: The fraction of rounds in which participants report their true preferences over prizes, listing all prizes, is 1 for all participants, and this does not depend on whether the participant or their competitors have access to the outside option prize, regardless of whether the outside option is integrated into the centralized system.
Hypothesis 2: Participants without access to the outside option prize should employ the same strategies across all unconstrained ROLs versions of the model, as they are expected to submit truthful ROLs of three prize types in each version. Similarly, participants with access to the outside option prize should not exhibit any differences in strategies across the unconstrained ROLs versions, as they should rank all the prizes available to them in the system truthfully and completely in every version.
Hypothesis 3: The resulting matchings are stable.
Constrained ROLs:
Hypothesis 4: The fraction of rounds in which participants submit partially true ROLs (preserving the original ranking of prizes from highest to lowest) of the maximum allowed length is 1 for all participants, regardless of whether they or their competitors have access to the outside option, and regardless of whether the outside option is integrated into the centralized prize distribution system.
In experimental groups where the outside option is integrated into the centralized system, participants who have access to the outside option will truthfully list it in all their submitted ROLs.
Hypothesis 5.1: In versions II.5) and II.7) of the model, where one-third of participants have access to the outside option prize, participants without the outside option are expected to submit a lower proportion of ROLs that include the top prize type A, compared to participants in the baseline model without the outside option.
Hypothesis 5.2: Integrating the outside option prize into the centralized system does not affect the mixing probabilities of various types of partial ROLs for participants without the outside option. That is, there are no expected differences in the share of ROLs that include the top prize type A for the participants without access to the outside option in versions II.5) and II.7) of the model.
Hypothesis 6: Participants with access to the outside option are more likely to list the top prize A as first priority on their ROLs compared to participants without access to the outside option.
Hypothesis 7: The percentage of stable matchings is less than 100%. Unlike the participants without the outside option, those with the outside option are never undermatched.
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Experimental Design (Public)
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Before
The main experiment will be conducted in a total of seven versions:
I. Unconstrained ROLs:
I.1) Control condition: no outside option for any participants;
I.2) Treatment: outside option is integrated (embedded) into the centralized system, available for 1/3 of participants;
I.3) Treatment: outside option is available for 1/3 of participants, but not integrated into the centralized system.
II. Constrained ROLs, participants can list only two out of the three available prize types:
II.1) Control condition: no outside option for any participants;
II.2) Treatment: outside option is integrated into the centralized system, available for 1/3 of participants;
II.3) Treatment: outside option is integrated into the centralized system, available for 2/3 of participants;
II.4) Treatment: outside option is available for 1/3 of participants, but not integrated into the centralized system.
The experiment will be conducted on paper. Each participant will take part in two versions of the experiment. For each version, participants will be required to submit 12 separate ROLs. The final winnings will be randomly determined based on one of the 12 submitted lists.
All participants will receive detailed instructions on the rules of the prize draw and an example of the DA algorithm. Following the instructions, the participants will take a quiz on the structure of the experiment and the DA algorithm. Since nearly all of the participating students are enrolled in the Principles of Microeconomics course, their quiz performance will earn bonus points towards their final Microeconomics course grade. Non-enrolled participants will be provided monetary incentives for successfully answering the quiz questions (up to 400 rubles or approximately $4.33).
Following the main experiment, participants will also complete a bomb risk elicitation task designed to assess their risk preferences. This additional task is included because the degree of risk aversion can influence the optimal strategies of the participants in the main experiment. The bomb risk elicitation task will be accompanied by financial incentives, with an expected average payout of 250 rubles ($2.71) per participant.
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After
The main experiment is conducted in a total of seven versions:
I. Unconstrained ROLs:
I.1) Control condition: no outside option for any participants;
I.2) Treatment: outside option is integrated (embedded) into the centralized system, available for 1/3 of participants;
I.3) Treatment: outside option is available for 1/3 of participants, but not integrated into the centralized system.
II. Constrained ROLs, participants can list only two out of the three available prize types:
II.4) Control condition: no outside option for any participants;
II.5) Treatment: outside option is integrated into the centralized system, available for 1/3 of participants;
II.6) Treatment: outside option is integrated into the centralized system, available for 2/3 of participants;
II.7) Treatment: outside option is available for 1/3 of participants, but not integrated into the centralized system.
The experiment is conducted on paper. Each participant takes part in two versions of the experiment. For each version, participants are required to submit 12 separate ROLs. The final winnings are randomly determined based on one of the 12 submitted lists. No feedback occurs between versions or rounds.
A simple example with two prize types (one prize of each type) and three participants is used to illustrate the workings of the algorithm. The example prizes are renamed (X and Y instead of A, B, and C), and the task focuses on the optimal decisions of the three example participants, using neutral language and avoiding direct advice to the participants themselves to prevent experimenter demand effects. Nevertheless, the logic and intuitions gained from this simpler context are emphasized as directly applicable to the one the participants would be part of during the main part of the experiment.
Following the instructions, the participants are tested to assess their understanding of the mechanism and optimal choices in the different versions of the experiment. Since nearly all the participating students are enrolled in the Principles of Microeconomics course, their test performance is incentivized with bonus points towards their final Microeconomics course grade. Non-enrolled participants are provided monetary incentives for successfully answering the quiz questions (up to 400 rubles or approximately $4.33).
Following the main experiment, participants also complete a bomb risk elicitation task designed to assess their risk preferences. This additional task is included because the degree of risk aversion can influence the optimal strategies of the participants in version II.6) of the experiment. The bomb risk elicitation task is accompanied by financial incentives, with an expected average payout of 250 rubles ($2.71) per participant.
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Additional Keyword(s)
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Before
Matching, school choice, student-proposing deferred acceptance mechanism, outside options
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After
matching markets; school choice; deferred acceptance mechanism; outside options
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