Inference for Matched Tuples and Fully Blocked Factorial Designs

by   Yuehao Bai, et al.

This paper studies inference in randomized controlled trials with multiple treatments, where treatment status is determined according to a "matched tuples" design. Here, by a matched tuples design, we mean an experimental design where units are sampled i.i.d. from the population of interest, grouped into "homogeneous" blocks with cardinality equal to the number of treatments, and finally, within each block, each treatment is assigned exactly once uniformly at random. We first study estimation and inference for matched tuples designs in the general setting where the parameter of interest is a vector of linear contrasts over the collection of average potential outcomes for each treatment. Parameters of this form include but are not limited to standard average treatment effects used to compare one treatment relative to another. We first establish conditions under which a sample analogue estimator is asymptotically normal and construct a consistent estimator of its corresponding asymptotic variance. Combining these results establishes the asymptotic validity of tests based on these estimators. In contrast, we show that a common testing procedure based on a linear regression with block fixed effects and the usual heteroskedasticity-robust variance estimator is invalid in the sense that the resulting test may have a limiting rejection probability under the null hypothesis strictly greater than the nominal level. We then apply our results to study the asymptotic properties of what we call "fully-blocked" 2^K factorial designs, which are simply matched tuples designs applied to a full factorial experiment. Leveraging our previous results, we establish that our estimator achieves a lower asymptotic variance under the fully-blocked design than that under any stratified factorial design. A simulation study and empirical application illustrate the practical relevance of our results.


page 1

page 2

page 3

page 4


Inference under Covariate-Adaptive Randomization with Multiple Treatments

This paper studies inference in randomized controlled trials with covari...

Inference in Experiments with Matched Pairs and Imperfect Compliance

This paper studies inference for the local average treatment effect in r...

Inference in Cluster Randomized Trials with Matched Pairs

This paper considers the problem of inference in cluster randomized tria...

On the Efficiency of Finely Stratified Experiments

This paper studies the efficient estimation of a large class of treatmen...

Revisiting the Analysis of Matched-Pair and Stratified Experiments in the Presence of Attrition

In this paper we revisit some common recommendations regarding the analy...

Estimation of Treatment Effects for Heterogeneous Matched Pairs Data with Probit Models

Estimating the effect of medical treatments on subject responses is one ...

Unifying Design-based Inference: On Bounding and Estimating the Variance of any Linear Estimator in any Experimental Design

This paper provides a design-based framework for variance (bound) estima...

Please sign up or login with your details

Forgot password? Click here to reset