Abstract: High frequency market makers (HFMMs) often serve as the dominant liquidity provider in equity, futures and, increasingly, other financial markets. They do so largely in the absence of constraints on their decisions to provide or remove liquidity, which they are able to modify on very short time scales. The question of how their liquidity provision can be expected to vary across different volatility regimes has significant implications for market stability. Do HFMMs provide less liquidity in extreme volatility environments? We address this question using a theoretical model with fully rational, optimizing HFMMs and provide empirical evidence.

プログラム2025年度

Abstract: This paper develops semiparametric Bayesian methods for estimating the average treatment effect on the treated (ATT) in difference-in-differences (DiD) designs. We propose two Bayesian procedures with frequentist validity. The first places a Gaussian process prior on the conditional mean function of the control group. The second is a double-robust Bayesian approach that adjusts the prior on the conditional mean function and then corrects the posterior distribution of the ATT. We establish a semiparametric Bernstein¨Von Mises theorem, showing the asymptotic equivalence between our Bayesian procedures and efficient frequentist estimators. For the second approach, the result holds under double-robust smoothness conditions: the lack of smoothness in the conditional mean function can be compensated by high regularity of the propensity score, and vice versa. Monte Carlo simulations and an empirical application demonstrate strong finite-sample performance of our Bayesian DiD methods. We also extend the Bayesian framework to staggered DiD designs.

Distributional Effects with Two-Sided Measurement Error: An Application to Intergenerational Income Mobility∗ (joint with Brantly Callaway, Irina Murtazashvili, Emmanuel S. Tsyawo)

Abstract: This paper considers identification and estimation of distributional effect parameters that depend on the
joint distribution of an outcome and another variable of interest (“treatment”) in a setting with “two-
sided” measurement error — that is, where both variables are possibly measured with error. Examples
of these parameters in the context of intergenerational income mobility include transition matrices, rank-
rank correlations, and the poverty rate of children as a function of their parents’ income, among others.
Building on recent work on quantile regression (QR) with measurement error in the outcome (particu-
larly, Hausman, Liu, Luo, and Palmer (2021)), we show that, given (i) two linear QR models separately
for the outcome and treatment conditional on other observed covariates and (ii) assumptions about the
measurement error for each variable, one can recover the joint distribution of the outcome and the treat-
ment. Besides these conditions, our approach does not require an instrument, repeated measurements,
or distributional assumptions about the measurement error. Using recent data from the 1997 National
Longitudinal Study of Youth, we find that accounting for measurement error notably reduces several
estimates of intergenerational mobility parameters.

Abstract: This talk will survey recent advances in understanding Chatterjee’s graph correlation coefficient. I will introduce, for the first time, a comprehensive theoretical framework for statistical inference based on this coefficient. The framework involves results on asymptotic normality, bias correction, and the (in)consistency of bootstrap methods.