This paper proposes a Bayesian approach to Multiple-Output Quantile Regression defined in Hallin et al. (2010). I prove consistency of the posterior and discuss interpretations of the prior. I apply the model to the Tennessee Project STAR experiment and find there is joint increase in the fixed-τ quantile regions for reading and math scores when there is a decrease in the number of students per teacher. This result is consistent with, and much stronger than, the result one would find with multivariate linear multiple regression. This paper can be viewed here.
In this paper I investigate if United States Supreme Court Justices recuse themselves strategically. A strategic recusal is when a Supreme Court justice might fail to remove themself from a case despite having a conflict of interest with the case. I create a new structural model for the Supreme Court recusal process. This is the first paper to use a structural approach to investigate strategic recusals. Using the model, I find evidence justices do recuse themselves strategically or perform some sort of `vote-switching' after a recusal. The evidence provided by this paper agrees with previous research. In a counterfactual simulation, under certain assumptions, I find that in a given year, at most 48% of cases have a justice who remains on the case despite having a conflict of interest. This paper can be viewed here.
I analyze the efficacy of Huber-White (sometimes called `robust') standard errors in the conditional logit model. There is little theoretical justification for using Huber-White standard errors in the conditional logit. If the model is misspecified, then the maximum likelihood estimator is consistent for the parameter minimizing Kullback-Leibler (KL) divergence of the assumed model from the data generating process. This KL minimizing parameter is generally not equivalent to the parameter of the data generating process (which is usually the parameter of interest). Thus the Huber-White standard errors are a correction for a parameter generally not of interest. I derive necessary and sufficient conditions for the when any misspecified Random Utility Model is consistent for the parameter of interest (when the KL minimizing parameter equals the data generating parameter). I also derive easily satisfied sufficient conditions for when the sign of the KL minimizer has the same sign as the data generating parameter. It follows that the researcher can consistently test the sign (or nullity) of the parameter from the data generating process using the (possibly) misspecified conditional logit. If the model is correctly specified, the maximum likelihood estimator is consistent and the Huber-White, hessian and outer product of gradient standard errors are equivalent (in expectation). If the model is misspecified and the maximum likelihood estimator is inconsistent, it is possible that the Huber-White standard error might still be preferable to the hessian standard error for non-null cofficients. I investigate this possibility in a simulation. Introducing incorrect specifications through failing to model 1) an alternative specific random effect and 2) a heteroskedastic effect. I find in some situations, intervals based on Huber-White standard errors perform slightly better than those based on hessian standard errors. However, Huber-White standard errors ultimately fail to correct for the misspecification and do not provide a practical advantage. Lastly, this paper provides a proof to pass a derivative twice inside the integral for the choice probability in the mixed logit. While this result is commonly used, it has never been formally proven. This paper can be viewed here.