Hello, I’m Zizhe Xia. Welcome to my personal site! I am 5-th year economics PhD student at Chicago Booth. I’m interested in mechanism design and information design.
How to pronounce my name?
Zizhe is pronounced like “zi-zhir” where “zh” is a retroflex consonant that sounds like a “j”, and “ir” sounds like in “firm”.
Xia is pronouced like “shia”.
Research
Comparisons of Information in Moral Hazard Problems
Abstract
I use a novel geometric approach to compare information in moral hazard problems. I study three nested geometric orders on information, namely the column space, the conic span, and the zonotope orders. The orders are defined by the inclusion of the column space, the conic span, and the zonotope of the matrices representing the experiments. For each order, I establish four equivalent characterizations – (i) inclusion of polyhedral sets of feasible state dependent utilities, (ii) matrix factorization, (iii) posterior belief distributions, and (iv) classes of moral hazard problems. The column space order characterizes the comparison of feasibility in all moral hazard problems. The conic span order characterizes the comparison of costs in all moral hazard problems with a risk neutral agent and limited liability. The zonotope order characterizes the comparison of costs in all moral hazard problems when the agent can have any utility exhibiting risk aversion.Expert Incentives under Non-Contractible States
Abstract
I study whether and which expert incentives can be provided at what cost when the states of the world become non-contractible, but there is some noisy observation about the states that can be contracted upon. A principal hires an agent to acquire costly information about the states, but it is not possible to pay the agent based on the realized states. Instead, the principal has access to a noisy (Blackwell) experiment about the states, and can pay bonuses based on its realization. The agent is risk neutral and protected by limited liability. I completely characterize what the principal can incentivize the agent to learn, and how to design contracts to minimize the costs to provide such incentives. I then study which contractible information is always better at incentive provision. This gives rise to a novel order on information. In the binary-binary case, this order is characterized by larger differences in the likelihood ratios of the two realizations. My results provide insights into what information is better for evaluating expert predictions.Screening Knowledge with Verifiable Evidence (with Sulagna Dasgupta)
Abstract
A principal seeks to screen an agent based on his demonstrable knowledge of a subject matter, modeled as a binary state. The agent learns about the state through two kinds of opposing verifiable signals, each kind providing evidence in favor of one of the states. A good quality agent has an evidence structure which is more informative than a bad quality one. In a symmetric setting, we show that under the optimal test, regardless of whether the agent can predict the state correctly, he is failed if the amount of evidence he is able to show is below a threshold. Conditional on providing evidence above this threshold, the agent is passed based on a simple True-False test – i.e., if and only if he gives the correct answer. We see this result as rationalizing a common test structure where test-takers are given credit for giving the correct answer only if they show a minimal amount of data, arguments, or steps, in support of their answer. We prove the results by identifying a connection to the optimal transport problem and leveraging it to show the existence of an appropriate virtual value function.Regulating Monopoly Quality without Transfers
Abstract
I study the extent to which a regulator can correct monopolistic distortions using quality and coverage regulations in the presence of asymmetric cost information. I characterize the optimal regulations that maximize the weighted surplus. When the monopolist tends to be inefficient, the optimal regulations entail setting a minimum quality standard (MQS) coupled with the universal coverage requirement. When the monopolist tends to be efficient, the optimal regulations set a quality cap for certain types. The monopolist is asked to either provide the maximum quality for all consumers, or he is not allowed to serve qualities above a certain level. If the regulator places enough welfare weight on monopoly profits, it is optimal to impose no regulation. In general, the optimal regulations feature both an MQS and a quality cap, and can be implemented with a regulatory menu offering at most three options. Additionally, I show that the regulator grants more flexibility to the monopolist as the welfare weight on monopoly profits increases.Contact
[First]-[Last] at chicagobooth.edu
Thank you for visiting!