Modern city governance relies heavily on crowdsourcing ("co-production") to identify problems such as downed trees and power lines. A major concern is that residents do not report problems at the same rates, with reporting heterogeneity directly translating to downstream disparities in how quickly incidents can be addressed. Measuring such under-reporting is a difficult statistical task, as, by definition, we do not observe incidents that are not reported or when reported incidents first occurred. Thus, low reporting rates and low ground-truth incident rates cannot be naively distinguished. We develop a method to identify (heterogeneous) reporting rates, without using external ground truth data. Our insight is that rates on $\textit{duplicate}$ reports about the same incident can be leveraged to disambiguate whether an incident has occurred with its reporting rate once it has occurred. Using this idea, we reduce the question to a standard Poisson rate estimation task -- even though the full incident reporting interval is also unobserved. We apply our method to over 100,000 resident reports made to the New York City Department of Parks and Recreation and to over 900,000 reports made to the Chicago Department of Transportation and Department of Water Management, finding that there are substantial spatial disparities in reporting rates even after controlling for incident characteristics -- some neighborhoods report three times as quickly as do others. These spatial disparities correspond to socio-economic characteristics: in NYC, higher population density, fraction of people with college degrees, income, and fraction of population that is White all positively correlate with reporting rates.

翻译：现代城市治理高度依赖众包（“共同生产”）来识别诸如倒伏树木和受损电线等问题。一个主要担忧是居民报告问题的比率存在差异，这种报告异质性会直接转化为事件响应速度的后续不平等。衡量这种漏报行为是一项困难的统计任务，因为根据定义，我们既无法观测到未被报告的事件，也无法得知已报告事件首次发生的具体时间。因此，低报告率与低真实事件发生率无法被简单区分。我们开发了一种方法，无需使用外部真实数据即可识别（异质性的）报告率。我们的核心见解在于：可以利用同一事件中重复报告的比率，来区分事件是否发生以及发生后其报告率的高低。基于这一思路，我们将问题简化为标准的泊松率估计任务——即便完整的事件报告区间同样未被观测到。我们将该方法应用于超过10万份向纽约市公园与娱乐局提交的居民报告，以及超过90万份向芝加哥交通局和水务管理局提交的报告。研究发现，即使在控制事件特征后，报告率仍存在显著的空间差异——某些社区的报告速率是其他社区的三倍。这些空间差异与社会经济特征相关：在纽约市，人口密度、拥有大学学位的人口比例、收入水平以及白人人口比例均与报告率呈正相关。