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Summary Point processes are probabilistic tools for modelling event data. While there exists a fast-growing literature on the relationships between point processes, how such relationships connect to causal effects remains unexplored. In the presence of unmeasured confounders, parameters from point process models do not necessarily have causal interpretations. We propose an instrumental variable method for causal inference with point process treatment and outcome. We define causal quantities based on potential outcomes and establish nonparametric identification results with a binary instrumental variable. We extend the traditional Wald estimation to deal with point process treatment and outcome, showing that it should be performed after a Fourier transform of the intention-to-treat effects on the treatment and outcome, and thus takes the form of deconvolution. We refer to this approach as generalized Wald estimation and propose an estimation strategy based on well-established deconvolution methods. 

Despite an increasing reliance on fully-automated algorithmic decision-making in our day-to-day lives, humans still make consequential decisions. While the existing literature focuses on the bias and fairness of algorithmic recommendations, an overlooked question is whether they improve human decisions. We develop a general statistical methodology for experimentally evaluating the causal impacts of algorithmic recommendations on human decisions. We also examine whether algorithmic recommendations improve the fairness of human decisions and derive the optimal decision rules under various settings. We apply the proposed methodology to the first-ever randomized controlled trial that evaluates the pretrial Public Safety Assessment in the United States criminal justice system. Our analysis of the preliminary data shows that providing the PSA to the judge has little overall impact on the judge’s decisions and subsequent arrestee behaviour.

 

Summary Instrumental variable methods can identify causal effects even when the treatment and outcome are confounded. We study the problem of imperfect measurements of the binary instrumental variable, treatment and outcome. We first consider nondifferential measurement errors, that is, the mismeasured variable does not depend on other variables given its true value. We show that the measurement error of the instrumental variable does not bias the estimate, that the measurement error of the treatment biases the estimate away from zero, and that the measurement error of the outcome biases the estimate toward zero. Moreover, we derive sharp bounds on the causal effects without additional assumptions. These bounds are informative because they exclude zero. We then consider differential measurement errors, and focus on sensitivity analyses in those settings.