Shuo Qi

ALT We study how policy-makers should set k policy instruments so as to best hit m (perhaps dynamic) targets, in a linear-quadratic model where there is statistical uncertainty about the causal effects of the policies. Plugging the estimated effects into "sufficient statistics" optimal policy formulas, as commonly done in the literature, can result in infinite risk. In fact, maintaining the status quo regardless of the data is uniquely minimax-optimal when m>1, and uniquely minimax-regret-optimal when m,k>1. Nevertheless, we recommend that policy-makers adopt a simple, dampened version of the popular plug-in rule, as in Fisher (1962) and Brainard (1967). Not only does this cautious rule outperform doing nothing over most of the parameter space, its worst-case risk is also close to the minimax value in empirically relevant models. Policy-makers should use causal effect estimates from an unbiased but dispersed estimator (such as a local projection) rather than from a moderately biased but pr

ALT We extend the indirect inference principle to structural econometric models that are incomplete, in the sense that a single value of the structural parameter may be compatible with multiple distributions of the observed endogenous variables, so that the structural parameter is typically only partially identified. We define the binding function as the smallest norm of the auxiliary estimating equations over the set of data generating processes compatible with the structural model. Hence, we obtain a confidence region by inverting a test of the hypothesis that the binding function vanishes at the pseudo-true value. A dual characterization based on random set theory makes the binding function computationally tractable. We define the auxiliary model conditionally on the covariates to remove its dependence on the unknown covariate distribution and we show that the binding function is Lipschitz and Hadamard directionally differentiable, so that the numerical delta method delivers valid criti

ALT This note contains a story and a paper. The paper is about the admissibility of two-stage least squares with weak instruments, a topic we have worked on together since 2019. The story is about how we (or, rather, our LLMs) wrote the paper, and some thoughts on what this may mean for our field.

ALT This paper proposes a nonparametric Bayesian inference framework for partially identified discrete response models. The key observation is that these models map a reduced-form conditional choice probability to an identified set. Consequently, nonparametric Bayesian inference for the conditional probability mass function leads to Bayesian inference for the identified set. The inference framework nests conditional moment inequalities and linear systems with unknown coefficients as special cases. Importantly, our proposal does not require converting conditional moments into unconditional moments or discretizing covariates. We show that the posterior is consistent for the true identified set when the model is correctly specified, show that the posterior can consistently detect model misspecification, and show posterior consistency for a pseudo-identified set that is valid under misspecification. We also verify the assumptions for a class of priors based on Gaussian processes that we use to

ALT Pairwise randomization can yield substantial efficiency gains in experiments. Yet methodological guidance cautions against pairwise randomization, especially in settings with attrition, partly because common practices for estimation (i.e., pair fixed effects) imply discarding data from incomplete pairs thus exacerbating data loss from attrition. This practice of dropping incomplete pairs reduces statistical power of tests as well as precision of estimates, in paired experiments, compared to designs with less finely stratified treatment assignment. We argue that this concern is misplaced if attrition is independent of treatment status and potential outcomes, and that these issues follow from an inefficient use of the data that remains post-attrition. First, we show how, by using a specific permutation test, it is possible to use all observed units for inference (complete pairs and incomplete pairs where one unit attrits) while still exploiting the pairwise randomization design structure

ALT We study how fast experimental designs can approach the semiparametric efficiency bound in finite samples, as measured by the excess variance of unadjusted treatment effect estimation. We prove an impossibility theorem: under weak conditions, no design can approach the variance bound uniformly over smooth outcome models unless covariate dimension d ≪ log n. Even in experiments with thousands of units, this permits only a handful of covariates. Motivated by this, we propose new designs based on discrepancy minimization that instead attempt to control imbalances over restricted-complexity nonparametric function classes. Such designs achieve fast rates to their corresponding restricted efficiency targets, permitting d ≪ n covariates in an additive nonparametric specification. They can also be combined with matching to protect against unmodeled outcome variation. In simulations calibrated to 12 published experiments, our designs reduce variance relative to matched pairs randomization in ev

ALT This paper considers design-based inference on the average treatment effect in finely stratified experiments, where uncertainty arises only from the randomized treatment assignment. We focus on settings in which units are first stratified into groups of fixed size according to baseline covariates and, then within each group, exactly one unit is assigned to treatment. In this setting, we introduce a class of graph-Laplacian variance estimators in which strata form the vertices of a weighted graph and edge weights determine how between-stratum comparisons are aggregated. The canonical estimator of Imai (2008) corresponds to a complete graph with edge weights normalized so that each stratum has weighted degree one, while a paired-stratum estimator arises from a perfect matching graph. For the subclass of degree-calibrated graphs, in which each vertex has weighted degree one, we derive an exact bias identity showing that the corresponding estimators are upward-biased, with bias governed by

ALT I study the optimal design and analysis of randomized experiments for estimating finite-population average treatment effects when potential outcomes are known to be bounded, as with binary outcomes. Among all assignment mechanisms and a broad class of affine estimators, worst-case mean-squared error (MSE) is minimized by independent random assignment and an unconventional regression of the support-midpoint-centered outcome on the recentered treatment, with no intercept. This contrasts with the usual prescription of balanced complete randomization and difference-in-means estimation: when outcomes are bounded, randomness in the realized treatment share is informative. The worst-case gain over full-sample complete randomization is asymptotically small, but gains can be first-order relative to other designs: complete within-pair randomization and pair-fixed-effect regression have twice the worst-case MSE. I extend the result to allow for arbitrary estimators. Independent random assignment

ALT This paper analyzes spillover effects in spatial (network) models when the neighborhood (adjacency) matrix is contaminated by measurement error from reporting, aggregation, or disclosure imperfections, leading to inconsistent estimation of network effects. We introduce a regularization framework for the latent network that allows for sparse and/or low-rank structure and accommodates potential correlation between measurement errors and outcomes. We propose two estimators: (i) a two-stage procedure that first denoises the adjacency matrix and then incorporates the purified network into a regression analysis, and (ii) a Generalized Method of Moments (GMM) estimator that jointly estimates regression parameters and refines the network structure. We then establish strictly improved consistency rates for the spillover effect estimator relative to naive estimation ignoring measurement error. Simulations demonstrate that, in the presence of noisy networks, our approach reduces the root mean squ