Luther Yap


Hi! I am a PhD candidate at Princeton University. My research interests are econometrics and applied microeconomics. You can view my CV here. Email:

Working Papers

Sensitivity Analysis of Policy Relevant Treatment Effects to Failures of Monotonicity

This paper proposes a method in an environment with heterogeneous treatment effects to bound policy relevant treatment parameters (PRTP) without the monotonicity assumption that the instrumental variable works in the same direction for all individuals. While the procedure applies to all PRTP objects, this paper provides a detailed analysis for local average treatment effects in counterfactual environments (LATE*) that does not yet have a procedure for sensitivity analysis to monotonicity violations. The bounding framework uses the proportion of defiers relative to compliers as a sensitivity parameter and yields an identified set that is an interval. The bounds are sharp for binary outcomes. The method is illustrated in an example where the same sex instrument is used to find the effect of having a third child on labor force participation. I find that bounds are informative only for small violations in monotonicity.


General Conditions for Valid Inference in Multi-Way Clustering

This paper proves a new central limit theorem for a sample that exhibits multi-way dependence and heterogeneity across clusters. Statistical inference for situations where there is both multi-way dependence and cluster heterogeneity has thus far been an open issue. Existing theory for multi-way clustering inference requires identical distributions across clusters (implied by the so-called separate exchangeability assumption). Yet no such homogeneity requirement is needed in the existing theory for one-way clustering. The new result therefore theoretically justifies the view that multi-way clustering is a more robust version of one-way clustering, consistent with applied practice. The result is applied to linear regression, where it is shown that a standard plug-in variance estimator is valid for inference.


Design-Based Justification for Clustering with Multiway Assignment

In causal inference, it is often not obvious what standard errors researchers should report, and what dimensions they should cluster the standard errors by, if at all. This paper provides a design-based perspective to when researchers should cluster when doing inference on the sample average treatment effect (ATE). By using the potential outcomes model, the researcher only has to consider randomness in the assignment mechanism to treatment, and can be agnostic about the data generating process for the outcome. This is advantageous when the process generating assignment is better understood than the process generating outcomes. The practical takeaway is that, when we are interested in the sample ATE, the only consideration on whether to cluster and which dimensions to cluster on is determined by assignment. Notably, this does not depend on the structure of the error term as is commonly argued in literature. Cluster on a particular dimension if and only if it affects assignment. Standard errors are conservative if we cluster on more dimensions than we have to. I illustrate the findings with a simple simulation and show consistency and asymptotic normality of standard estimators in this design-based framework.

Market Design, Subsidies, and Supply: Interventions for Efficient and Equitable Public Housing

(with Andrew Ferdowsian and Kwok-Hao Lee)

We study how public housing can be allocated more efficiently and equitably, comparing market design interventions to subsidies and changing the mix of apartments available. To this end, we combine tools from Urban Economics and Industrial Organization to formulate a dynamic choice model over housing lotteries. Our model is estimated on novel public housing data from the Singaporean mechanism, in which bigger apartments are sold at larger markdowns from their resale price to ensure affordability. We find that each rich household receives an average of 1.5 times the amount of subsidy that poor households receive, precisely because they opt for these larger apartments. Then, we simulate outcomes for households applying for apartments under various counterfactual mechanisms. We find that: first, if the social planner does not expand supply, it is difficult to reduce wait times in this mechanism. Second, to raise match rates for the poor, the government should subsidize them and increase prices on the largest apartments; in this policy regime, subsidies are redistributed 1-for-1 from the rich to the poor. Third, by prioritizing the poor, the government can improve their “match quality” without worsening that of the rich. Finally, building more, smaller apartments (in lieu of larger ones) results in congestion, raising wait times for the rich and lowering match rates for the poor.


Build to Order: Endogenous Supply in Centralized Mechanisms

(with Andrew Ferdowsian and Kwok-Hao Lee)

How should the supply of public housing be optimally curated? Queuing mechanisms in the literature treat the supply of goods as exogenous. However, in practice, designers can often control the inflow of goods as well. We study a dynamic matching model based on the Singaporean housing allocation process. We show that endogenous supply radically changes the nature of the optimal mechanism. In this mechanism, a key feature is that under-demanded housing is overproduced relative to the static benchmark. Though competition leads to a decrease in efficiency when supply is exogenous, competition instead improves matching when supply is endogenous. Competition can be artificially generated through increasing the thickness of the market by batching applications. We show that doing so is a key feature of the optimal mechanism when the planner places a high weight on match quality.


Works in Progress

“Valid t-ratio in Overidentified Two-Stage Least Squares Instrumental Variables Designs”. With David Lee, Justin McCrary, Marcelo Moreira, and Jack Porter.