Could you spare me a moment? A model of primary data collection by statistics institutes

We study the strategic interaction between a statistical institute and a survey respondent (either a firm or a household). The respondent must decide whether to acquire the information required by the institute, thereby incurring a private cost. After receiving the reported data, the institute chooses whether to audit the respondent's declaration. The key innovation of our model is to introduce two-sided asymmetric information: both the cost of acquiring the information and the cost of auditing are private and known only to the respective agent. We characterize a Perfect Bayesian equilibrium and show that there is substitutability between the magnitude of the punishment for misreporting and the probability of auditing. Our framework allows for both positive and normative analysis of the challenges faced by statistical agencies in data collection, providing insights into how enforcement mechanisms can be designed to balance deterrence and audit costs.