Curriculum Vitae
Rongzhu Ke


Assistant Professor, Department of Economics, the Chinese University of Hong Kong.


Primary Fields: Applied Micro Theory, Applied Econometrics. Secondary Fields: Organizational
economics, Political Economics.


Ph.D in Economics, MIT, USA, 2004-2009.
M.A in Economics, Zhejiang University, Zhejiang, China, 1998-2001.
B.A. in Economics, Zhejiang University, Zhejiang, China, 1994-1998.


Basic Microeconomics (ECON2011B), Graduate Thesis Research (ECON8006).

  1. "Identification of Moral Hazard Problems: First Order Approach and Statistical Inference"
    Abstract: This paper develops a non-parametric methodology for identifying moral hazard problem, based on the first order condition (known as the Mirrlees-Holmstrom Condition (MHC)) of contract optimality in a standard principal-agent model (Holmstrom, 1979). We show that the MHC is equivalent to the attainment of the Cramer-Rao Lower Bound (CRLB) of estimating marginal incentive cost. Therefore, a non-parametric testing for contract optimality is a correlation coefficient test between inverse marginal utility and the score function with respect to the nuisance effort parameter. The test is non-parametric in a sense that the contractual form, monetary utility, cost function of effort, the distribution of output, or the score function are unknown. We show that the agent's inverse marginal utility can be identified up to an affine transformation, under the null hypothesis. Meanwhile, we also propose an estimator for the loss of profit, compared with the second best counterfactual. In addition, the present approach is applied to test optimality and estimate bounds on the loss of profit for a piece-rate contract adopted by a cotton weaving factory in Zhejiang Province, China.

  2. "Fixed-Point Method for Validating the First-Order Approach"
    Abstract: We propose a fixed-point method for validating the first-order approach (FOA). Instead of checking the global concavity of the agent's expected utility, we directly verify the existence of a fixed point of the agent's best reaction to the principal's targeted effort level. This condition is in fact a necessary and sufficient condition for validating the FOA. The new method allows the relaxation of several requirements of previous approaches (e.g., global concavity of the agent's expected utility or monotonicity of payment). We show a canonical set of sufficient conditions for validating the FOA under the utility restriction proposed by Jewitt (1988), where the agent's expected utility is not globally concave but supermodular. A large class of exponential family distributions satisfy the new sufficient condition, although such distributions cannot be justified in Jewitt's original approach. We also generalize the main results of Sinclair-Desgagne (1994) and Conlon (2009a) to accommodate non-separable utility and non-monotonicity of payment. Thus the FOA is valid for either the mixture probability model without the likelihood ratio order, or certain exponential family distributions with a bounded likelihood ratio.

  3. "A Fixed-Point Method for Solving the Principal-agent Problems: Beyond the First-Order Approach"
    Abstract: This paper generalizes Ke's (2010) fixed-point method and develops a unified solution method for principal-agent problems with moral hazard under a general setting (i.e., multi-task and multi-signal). We show that the principal's problem with a complicated incentive compatibility constraint, which consists of infinitely many inequalities, is equivalent to a Lagrangian dual problem with routine equality and inequality constraints. The discovered Lagrangian dual representation only includes the least necessary constraints for individual rationality and incentive compatibility. Thus, we can characterize the optimal contract and solve the principal-agent problem by a routine parametric programming. We provide a set of Kuhn-Tucker optimality conditions that can be applied to find a solution, regardless of the validity of the first-order approach. We also provide some examples and comparative static analysis.

  4. "Auctioning Social Surplus: A Best Possible Bayesian Mechanism with Ex Post Budget Balance".
    Abstract: In a classical environment, this paper investigates the existence and properties of the best possible Bayesian incentive compatible mechanism in the sense that it is ex post budget balance, ex post individually rational and maximizes the possibility of ex post incentive compatibility. We show that in private good cases (symmetric independent distribution), such a mechanism exists and is generically unique whenever the VCG mechanism runs expected surplus. In addition, compared with standard auctions, the mechanism generates a risk-free revenue to the seller and ex post individually rational payoff to the bidders. In public good case, we show that the main conclusion carries through in two-player case. But for n-player case, some further restrictions on primitives are required. We also apply our construction to explore the existence of bilateral trade mechanism, considering the interplay among divisibility, endowment distribution and preference. Two new findings are: first when the ex post individual rationality is imposed on, we obtain a stronger version of impossibility proposition (e.g., no efficient partner dissolving mechanism). Second, we identify a set of sufficient condition for the existence of a best possible trade mechanism.

  5. "Optimal Wage Commitment under Career Concern"
    Abstract: This paper explores the optimal time pattern of wage commitment in a career concern framework. It is shown that by choosing the appropriate length of wage commitment the over-signaling problem in Holmstrom (1982) can be alleviated, and efficiency can be improved. We prove that in a general n-period discrete model, given that the social welfare function is super concave (maximized value of a concave function is also concave in exogenous parameters), updating the wage period by period is optimal when the effort level is below the first best one. However, the optimal wage commitment deviates from the time pattern in the classical model when the effort is above the first-best level. This paper also shows that the first best effort level can be restored if severance pay is allowed to be contingent on past history of employment.

  6. "The Insurance Role of Rosca in the Presence of Credit Markets: Theory and Evidence" (Joint with Hanming Fang and Li-an Zhou).
    Abstract: Rotating Savings and Credit Associations (Roscas) are an important informal financial institution in many parts of the world. Existing models of Roscas assume that their participants do not have access to formal financial markets and predict that the implicit interest rates in bidding Roscas should be declining over their lives. Evidence from survey and field data sets from Wenzhou of Zhejiang Province in Southeastern China shows instead that Roscas are prevalent even in the presence of formal financial markets and more interestingly a large fraction of Rosca participants reported borrowing from the formal credit market to fulfill their Rosca obligations and saving their extra Rosca earnings in the formal credit market. Moreover, we find that the implicit interest rates observed in a unique Rosca bidding data set are not monotonically declining over its life. We develop a sequential auction model of risk averse Rosca participants facing income risks to investigate the interaction between formal and informal financial institutions to provide a possible explanation of the above two phenomena in the Chinese data. In this model, a Rosca provides insurance to its participants even in the presence of formal credit markets. The intuition is that while the formal credit market allows individuals to smooth their intertemporal income risks by borrowing and saving, a Rosca provides an additional instrument for its participants to share contemporaneous income. We also show that in this model it is possible that the implicit interest rate in equilibrium may not be declining over the life of a Rosca.

  7. "Extreme Bonus Does not Work: the Existence of Optimal Deterministic Contracts in Pure Moral Hazard Problems"
    Abstract: This paper investigates the existence of a deterministic solution to pure moral hazard problems under a rather general setting, given that the principal's and agent's utilities are concave in monetary payment. We show that as long as the agent's utility is bounded from below by some integrable function (e.g., limited liability), it is no longer possible to have an asymptotic first best solution when the non-existence of the optimal contract occurs. We further show that the boundedness of the agent's utility from below suffices for the existence of an optimal contract. So it is unnecessary to have a priori uniform boundedness and weak sequential compactness restrictions on the contract space. Therefore, we justify a classical intuition (Holmstrom, 1977) that the extreme bonus scheme cannot approach the first best, nor the second best.

  1. A Non-linear Lagrangian Approach to Address the Issue of the Duality Gap: Theory and Algorithm.
  2. A Dual Equivalent Representation for Multi-level Programming.
  3. Existence and Uniqueness of Time-Consistent Markov Perfect Equilibria (with Song Zheng).
  4. Economic Growth under Moral Hazard: Theory and Evidence.
  5. Optimal Tournament under Moral Hazard (with Jin Li).