# Research

**Published or Forthcoming**

1. (2021). “Inference for Experiments with Matched Pairs” (with Y. Bai and J. P. Romano), forthcoming in the *Journal of the American Statistical Association.* (pdf). Supplementary Appendix (pdf)

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2. (2019) “The Wild Bootstrap with a “Small” Number of “Large” Clusters” (with I. A. Canay and A. Santos), forthcoming in the *Review of Economics and Statistics* (pdf).

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3. (2019) “Inference under Covariate-Adaptive Randomization with Multiple Treatments” (with F. Bugni and I. A. Canay), *Quantitative Economics*, Vol. 10, Iss. 4, p. 1747–1785 (pdf).

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4. (2019) “Instrumental Variables and the Sign of the Average Treatment Effect” (with C. Machado and E. J. Vytlacil), *Journal of Econometrics*, Vol. 212, Iss. 2, p. 522–555 (pdf).

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5. (2019) “Multiple Testing in Experimental Economics” (with J. A. List and Y. Xu), *Experimental Economics*, Vol. 22, Iss. 4, p. 773–793 (pdf).

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6. (2018) “The Econometrics of Shape Restrictions” (with D. Chetverikov and A. Santos), *Annual Review of Economics*, Vol. 10, p. 31-63 (pdf).

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7. (2018) “Inference under Covariate-Adaptive Randomization” (with F. Bugni and I. A. Canay), *Journal of the American Statistical Association*, Vol. 113, Iss. 524, p. 1784-1796 (pdf).

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8. (2017) “Keeping the ECON in Econometrics: (Micro-)Econometrics in the *Journal of Political Economy*” (with S. Bonhomme), forthcoming in the *Journal of Political Economy (Special Issue on the 125th Anniversary of the Journal)*, Vol. 125, Iss. 6, p. 1846-1853. (pdf).

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9. (2017) “Practical and Theoretical Advances for Inference in Partially Identified Models” (with I. A. Canay), in B. Honore, A. Pakes, M. Piazzesi, & L. Samuelson, eds., *Advances in Economics and Econometrics: 11th World Congress (Econometric Society Monographs)*, p. 271-306 (pdf).

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10. (2017) “Randomization Tests under an Approximate Symmetry Assumption” (with I. A. Canay and J. P. Romano), *Econometrica*, Vol. 85, No. 3, p. 1013-1030 (pdf). Supplementary Appendix (pdf).

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11. (2014) “Multiple Testing and Heterogeneous Treatment Effects: Re-evaluating the Effect of PROGRESA on School Enrollment” (with S. Lee), *Journal of Applied Econometrics*, Vol. 29, Iss. 4, p. 612-626 (pdf).

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12. (2014) “A Practical Two-Step Method for Testing Moment Inequalities” (with J. P. Romano and Michael Wolf), *Econometrica*, Vol. 82, No. 5, p. 1979-2002 (pdf). Supplementary Appendix (pdf).

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13. (2013) “On the Testability of Identification in Some Nonparametric Models with Endogeneity” (with I. A. Canay and A. Santos), *Econometrica*, Vol. 81, No. 6, p. 2535-2559 (pdf).

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14. (2012) “On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions” (with Y. Kitamura and A. Santos), *Econometrica*, Vol. 80, No. 1, p. 413-423 (pdf). Supplemental Appendix (pdf).

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15. (2012) “Treatment Effect Bounds: An Application to Swan-Ganz Catheterization” (with J. Bhattacharya and E. J. Vytlacil), *Journal of Econometrics*, Vol. 168, Iss. 2, p. 223-243 (pdf).

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16. (2012) “On the Uniform Asymptotic Validity of Subsampling and the Bootstrap” (with J. P. Romano), *Annals of Statistics*, Vol. 40, No. 6, p. 2798-2822 (pdf). Supplementary Appendix (pdf).

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17. (2011) “Consonance and the Closure Method in Multiple Testing” (with J. P. Romano and Michael Wolf), *International Journal of Biostatistics*, Vol. 7, Iss. 1, Art. 12 (pdf).

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*s*null hypotheses simultaneously. In order to deal with the multiplicity problem, the classical approach is to restrict attention to multiple testing procedures that control the familywise error rate (FWE). The closure method of Marcus et al. (1976) reduces the problem of constructing such procedures to one of constructing single tests that control the usual probability of a Type 1 error. It was shown by Sonnemann (1982, 2008) that any coherent multiple testing procedure can be constructed using the closure method. Moreover, it was shown by Sonnemann and Finner (1988) that any incoherent multiple testing procedure can be replaced by a coherent multiple testing procedure which is at least as good. In this paper, we first show an analogous result for dissonant and consonant multiple testing procedures. We show further that, inmany cases, the improvement of the consonant multiple testing procedure over the dissonantmultiple testing procedure may in fact be strict in the sense that it has strictly greater probability of detecting a false null hypothesis while still maintaining control of the FWE. Finally, we show how consonance can be used in the construction of some optimal maximin multiple testing procedures. This last result is especially of interest because there are very few results on optimality in the multiple testing literature.

18. (2011) “Partial Identification in Triangular Systems of Equations with Binary Dependent Variables” (with E. J. Vytlacil), *Econometrica*, Vol. 79, No. 3, p. 949-955 (pdf). Supplemental Appendix (pdf).

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19. (2010) “Inference for the Identified Set in Partially Identified Econometric Models” (with J. P. Romano), *Econometrica*, Vol. 78, No. 1, p. 169-211 (pdf).

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20. (2010) “Hypothesis Testing in Econometrics” (with J. P. Romano and Michael Wolf), *Annual Review of Economics*, Vol. 2, p. 75-104 (pdf).

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21. (2010) “Multiple Testing” (with J. P. Romano and Michael Wolf), *New Palgrave Dictionary of Economics (Online Edition)* (pdf).

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22. (2009) “A Specification Test for the Propensity Score using its Distribution Conditional on Participation” (with M. Simonsen, E. J. Vytlacil, and N. Yildiz), *Journal of Econometrics*, Vol. 151, Iss. 1, p. 33-46 (pdf).

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23. (2008) “Endogenous Binary Choice Models with Median Restrictions: A Comment” (with E. J. Vytlacil), *Economics Letters*, Vol. 98, Iss. 1, p. 23-28 (pdf).

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24. (2008) “Formalized Data Snooping Based on Generalized Error Rates” (with J. P. Romano and Michael Wolf), *Econometric Theory*, Vol. 24, Iss. 2, p. 404-447 (pdf).

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25. (2008) “Treatment Effect Bounds under Monotonicity Assumptions: An Application to Swan-Ganz Catheterization” (with J. Bhattacharya and E. J. Vytlacil), *American Economic Review Papers and Proceedings*, Vol 98, No. 2, p. 351-356 (pdf).

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We use these different approaches to study the effects of Swan-Ganz catheterization on patient mortality. In Section I, we describe each of the resulting bounds when there are no other exogenous covariates that directly affect the outcome. We show that if the effect of the treatment is positive and the assumptions of SV hold, then the bounds of SV coincide with those of MP that assume a priori that the effect of the treatment is positive. If the effect of the treatment is instead negative and the assumptions of SV hold, then the bounds of SV coincide with those of MP that assume a priori that the effect of the treatment is negative.Hence, the trade-off between the analyses of SV and MP in the case of no exogenous covariates besides the instrument is that the latter requires one to know a priori whether the effect of the treatment is positive or negative, while the former requires one to impose monotonicity of the treatment in the instrument in order to be able to determine the sign of the treatment effect from the distribution of the observed data. If there are exogenous regressors that vary conditional on the 0tted value of the treatment, then the SV bounds become much narrower than the MP bounds. We show further that it is not possible to determine the sign of the treatment effect in the same way as SV under the assumptions of MP. Current work by Cecilia Machado, Shaikh, and Vytlacil (2008) develops the sharp bounds for the average treatment effect under the restriction that the outcome is monotone in the treatment, but without assuming the direction of the monotonicity a priori or that the treatment is monotone in the instrument. In Section II, we construct bounds on the average effect of Swan-Ganz catheterization on patient mortality under each of these three sets of assumptions. The data used are the same as in the influential observational study on the effect of Swan-Ganz catheterization on patient mortality by A. Connors et al. (1996). This study assumes that there are no unobserved differences between patients who are catheterized and patients who are not catheterized, and finds that catheterization increases patient mortality180 days after admission to the intensive care unit (ICU). The three approaches describedabove permit such differences, but require an instrument. We propose and justify the use of an indicator for weekend admission to the ICU as an instrument for catheterization in this context. Under the assumptions of SV, Bhattacharya, Shaikh, and Vytlacil (2005) find that catheterization increases patient mortality at all time horizons beyond seven days after admission to the ICU. We expand this analysis here to consider the assumptions of MP.

26. (2008) “Inference for Identifiable Parameters in Partially Identified Econometric Models” (with J. P. Romano), *Journal of Statistical Planning and Inference (Special Issue in Honor of T. W. Anderson, Jr. on the Occasion of his 90th Birthday)*, Vol. 138, Iss. 9, p. 2786-2807 (pdf).

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*Q (θ,P)*for

*θ ε Θ*. The second argument indicates the dependence of the objective function on

*P*, the distribution of the observed data. Unlike the classical extremum estimation framework, it is not assumed that

*Q (θ,P)*has a unique minimizer in the parameter space

*Θ*. The goal may be either to draw inferences about some unknown point in the set of minimizers of the population objective function or to draw inferences about the set of minimizers itself. In this paper, the object of interest is some unknown point

*θ ε Θ0(P)*, where

*Θ*, and so we seek random sets that contain each

_{0}(P)=arg min_{θ}ε_{Θ }Q(θ,P)*θ ε Θ*with at least some prespecified probability asymptotically. We also consider situations where the object of interest is the image of some point

_{0}(P)*θ ε Θ*under a known function. Computationally intensive, yet feasible procedures for constructing random sets satisfying the desired coverage property under weak assumptions are provided. We also provide conditions under which the confidence regions are uniformly consistent in level.© 2008 Elsevier B.V. All rights reserved.

_{0}(P)27. (2008) “Control of the False Discovery Rate under Dependence using the Bootstrap and Subsampling (with Discussion and Rejoinder)” (with J. P. Romano and Michael Wolf), *TEST*, Vol. 17, No. 3, p. 417-442 (pdf) and 461-471 (pdf).

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28. (2008) “Discussion: On Methods Controlling the False Discovery Rate” (with J. P. Romano and Michael Wolf), *Sankya*, Vol. 70, Part 2, p. 169-176 (pdf).

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29. (2006) “On Stepdown Control of the False Discovery Proportion” (with J. P. Romano), in J. Rojo, ed., *IMS Lecture Notes – Monograph Series, 2nd Lehmann Symposium – Optimality*, Vol. 49, p. 33-50 (pdf).

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*FW ER*), the probability of even one false rejection. However, if s is large, control of the

*FW ER*is so stringent that the ability of a procedure which controls the

*FW ER*to detect false null hypotheses is limited. Consequently, it is desirable to consider other measures of error control. We will consider methods based on controlof the false discovery proportion (

*F DP*) defined by the number of false rejections divided by the total number of rejections (defined to be 0 if there are no rejections). The false discovery rate proposed by Benjamini and Hochberg (1995) controls

*E(F DP)*. Here, we construct methods such that, for any γ and α,

*P{F DP > γ}*≤ α. Based on p-values of individual tests, we consider stepdown procedures that control the

*F DP*, without imposing dependence assumptions on the joint distribution of the p-values. A greatly improved version of a method given in Lehmann and Romano [10] is derived and generalized to provide a means by which any sequence of nondecreasing constants can be rescaled to ensure control of the

*F DP*. We also provide a stepdown procedure that controls the F DR under a dependence assumption.

30. (2006) “Stepup Procedures for Control of Generalizations of the Familywise Error Rate” (with J. P. Romano), *Annals of Statistics*, Vol. 34, No. 4., p. 1850-1873 (pdf).

### Abstract

*FWER*), the probability of even one false rejection. But if

*s*is large, control of the

*FWER*is so stringent that the ability of a procedure that controls the

*FWER*to detect false null hypotheses is limited. It is therefore desirable to consider other measures of error control. This article considers two generalizations of the

*FWER.*The first is the

*k-FWER*, in which one is willing to tolerate k or more false rejections for some fixed k ≥ 1. The second is based on the false discovery proportion (

*FDP*), defined to be the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289–300] proposed control of the false discovery rate (

*FDR*), by which they meant that, for fixed α,

*E(FDP)*≤ α. Here, we consider control of the

*FDP*in the sense that, for fixed γ and α,

*P{FDP > γ}*≤ α. Beginning with any nondecreasing sequence of constants and p-values for the individual tests, we derive stepup procedures that control each of these two measures of error control without imposing any assumptions on the dependence structure of the p-values. We use our results to point out a few interesting connections with some closely related stepdown procedures. We then compare and contrast two

*FDP*-controlling procedures obtained using our results with the stepup procedure for control of the

*FDR*of Benjamini and Yekutieli [Ann. Statist. 29 (2001) 1165–1188].

**Submitted for Publication**

31. (2021) “A User’s Guide to Approximate Randomization Tests with a Small Number of Clusters” (with Y. Cai, I. A. Canay and D. Kim), submitted (pdf).

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32. (2021) “A Two-Step Method for Testing Many Moment Inequalities” (with Y. Bai and A. Santos), resubmitted to the *Journal of Business and Economic Statistics* (pdf).

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33. (2020) “Inference for Large-Scale Linear Systems with Known Coefficients” (with Z. Fang, A. Santos and A. Torgovitsky), revision requested by *Econometrica* (pdf).

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34. (2020) “Inference with Imperfect Randomization: The Case of the Perry Preschool Program” (with J. Heckman, and R. Pinto), revision requested by the *Journal of Econometrics* (pdf).

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35. (2020) “Inference for Ranks with Applications to Mobility across Neighborhoods and Academic Achievement across Countries” (with M. Mogstad, J. P. Romano, and D. Wilhelm), revision requested by the *Review of Economic Studies* (pdf).

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36. (2020) “Randomization Tests in Observational Studies with Time-varying Adoption of Treatment” (with P. Toulis), resubmitted to the *Journal of the American Statistical Association* (pdf).

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**Working Papers**

37. (2020) “Partial Identification of Treatment Effect Rankings with Instrumental Variables” (with Y. Bai and E. J. Vytlacil), working paper (pdf).

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38. (2004) “Electricity Regulation in California and Input Market Distortions” (with M. Jacobsen), Stanford Institute for Economic Policy Research Discussion Paper 03-016 (pdf).

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### Acknowledgements

Financial support from the Stanford Institute for Economic Policy Research, the National Science Foundation and the Alfred P. Sloan Foundation is gratefully acknowledged. Parts of the above research were conducted while in residence at the Cowles Foundation for Research in Economics and the Hoover Institution at Stanford University.