Economic Theory Commons^™

Efficiency, Quality Of Forecasts And Radner Equilibria, Shurojit Chatterji, Atsushi Kajii

Research Collection School Of Economics

We study a simple two period economy with no uncertainty and complete markets where agents trade based on forecasts about the second period spot price. We propose as our solution concept a set of forecasts with the following properties: there exist (heterogenous) forecasts contained in this set that lead to efficient allocations, the set contains only those forecasts that correspond to some efficient equilibrium, and Önally that the forecasts assign positive probability to the actual market clearing spot price. We call such a set of prices an efficient equilibrium with ambiguity, and interpret it as a generalization of Radner equilibrium …

Random Assignment Of Bundles, Shurojit Chatterji, Peng Liu

Research Collection School Of Economics

We propose a model studying the random assignments of bundles with no free disposal. The key difference between our model and the one where objects are allocated (see Bogomolnaia and Moulin (2001)) is one of feasibility. The implications of this difference are significant. Firstly, the characterization of sd-efficient random assignments is more complex. Secondly, we are able to identify a preference restriction, called essential monotonicity, under which the random serial dictatorship rule (extended to the setting with bundles) is equivalent to the probabilistic serial rule (extended to the setting with bundles). This equivalence implies the existence of a rule on …

Random Assignments Of Bundles, Shurojit Chatterji, Liu Peng

Research Collection School Of Economics

We propose a model studying the random assignments of bundles with no free disposal. The key difference between our model and the one where objects are allocated (see Bogomolnaia and Moulin (2001)) is one of feasibility. The implications of this difference are significant. Firstly, the characterization of sd-efficient random assignments is more complex. Secondly, we are able to identify a preference restriction, called essential monotonicity, under which the random serial dictatorship rule (extended to the setting with bundles) is equivalent to the probabilistic serial rule (extended to the setting with bundles). This equivalence implies the existence of a rule on …

The Relative Price Of Capital And Economic Structure, Roberto Samaniego, Juliana Yu Sun

Research Collection School Of Economics

Are trends in the price of capital technological in nature? First, we find that trends in the relative price of capital vary significantly across countries. We then show that a multi-industry growth model, calibrated to match differences in economic structure around the world and productivity growth rates across industries, accounts for this variation – mainly due to variation in the composition of capital. The finding indicates that the rate of change in the relative price of capital can be interpreted as investment-specific technical change – the extent to which productivity growth is relatively more rapid in the capital-producing sector. The …

Preferences With Changing Ambiguity Aversion, Jingyi Xue

Research Collection School Of Economics

We provide two extensions of Gilboa and Schmeidler (J Math Econ 18:141–153, 1989)’s maxmin expected utility decision rule to accommodate a decision maker’s changing ambiguity attitudes. The two rules are, respectively, a weighted maxmin rule and a variant constraint rule. The former evaluates an act by a weighted average of its worst and best possible expected utilities over a set of priors, with the weights depending on the act. The latter evaluates an act by its worst expected utility over a neighborhood of a set of approximating priors, with the size of the neighborhood depending on the act. Canonical representations …

Restricted Probabilistic Fixed Ballot Rules And Hybrid Domains, Shurojit Chatterji, Souvik Roy, Soumyarup Sadhukhan, Arunava Sen, Huaxia Zeng

Research Collection School Of Economics

We study Random Social Choice Functions (or RSCFs) in a standard ordinal mech-anism design model. We introduce a new preference domain called a hybrid domain which includes as special cases as the complete domain and the single-peaked domain. We characterize the class of unanimous and strategy-proof RSCFs on these domains and refer to them as Restricted Probabilistic Fixed Ballot Rules (or RPFBRs). These RSCFs are not necessarily decomposable, i.e., cannot be written as a convex combina-tion of their deterministic counterparts. We identify a necessary and sufficient condition under which decomposability holds for anonymous RPFBRs. Finally, we provide an axiomatic justification …

The Economist’S Vision For 2020, Singapore Management University

Perspectives@SMU

The global economy will have stable but sluggish growth due to the macro environment

Rationalizable Incentives: Interim Implementation Of Sets In Rationalizable Strategies, Takashi Kunimoto, Roberto Serrano

Research Collection School Of Economics

This paper investigates rationalizable implementation of social choice sets (SCSs) in incomplete information environments. We identify rationalizable incentive compatibility (RIC) as its key condition, argue by means of example that RIC is strictly weaker than the standard Bayesian incentive compatibility (BIC), and show that RIC reduces to BIC when we only consider single-valued SCSs (i.e., social choice functions or SCFs). We next identify additional necessary conditions and, essentially closing the gap be-tween necessity and sufficiency, obtain a sufficiency result for rationalizable implementation in general environments. We also characterize a well-studied class of economic environments in which RIC is essentially the …

Kick-Starting Economic Growth: An Interview With Dr K. V. Subramanian, India's Chief Economic Advisor, K V Subramanian, Havovi Joshi

Asian Management Insights

Dr K. V. Subramanian emphasises the importance of higher investment rates, good quality loans, and structural reforms for boosting India’s economic growth.

Rationalizable Implementation Of Correspondences, Takashi Kunimoto, Roberto Serrano

Research Collection School Of Economics

A new condition, which we call uniform monotonicity, is shown to be necessary and almost sufficient for rationalizable implementation of corre-spondences. Uniform monotonicity is much weaker than Maskin monotonic-ity and reduces to it in the case of functions. Maskin monotonicity, the key condition for Nash implementation, had also been shown to be necessary for rationalizable implementation of social choice functions. Our conclusion is that the conditions for rationalizable implementation are not only starkly different from, but also much weaker than those for Nash implementation, when we consider social choice correspondences. Thus, dropping rational ex-pectations significantly expands the class of rules …

Strategically Simple Mechanisms, Tilman Börgers, Jiangtao Li

Research Collection School Of Economics

We define and investigate a property of mechanisms that we call "strategic simplicity," and that is meant to capture the idea that, in strategically simple mechanisms, strategic choices require limited strategic sophistication. We define a mechanism to be strategically simple if choices can be based on first-order beliefs about the other agents' preferences and first-order certainty about the other agents' rationality alone, and there is no need for agents to form higher-order beliefs, because such beliefs are irrelevant to the optimal strategies. All dominant strategy mechanisms are strategically simple. But many more mechanisms are strategically simple. In particular, strategically simple …

Parametric Rationing With Uncertain Needs, Yan Long, Jingyi Xue

Research Collection School Of Economics

We study resource allocation in the face of uncertain needs. We extend Young (1987)’s parametric rules to the uncertain context. We re-establish the axiomatic char-acterization of parametric rules and show the optimality of the rules.

Non-Separable Models With High-Dimensional Data, Liangjun Su, T Ura, Yc Zhang

Research Collection School Of Economics

This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and potentially larger than the effective sample size. We propose a three-step estimation procedure to estimate the average, quantile, and marginal treatment effects. In the first stage we estimate the conditional mean, distribution, and density objects by penalized local least squares, penalized local maximum likelihood estimation, and numerical differentiation, respectively, where control variables are selected via a localized method of L-1-penalization at each value of the continuous treatment. In the second stage we estimate the average and marginal distribution of the potential …

Continuous Implementation With Small Transfers, Yi-Chun Chen, Takashi Kunimoto, Yifei Sun

Research Collection School Of Economics

The robust mechanism design literature investigates the global robustness of op-timal mechanisms to large changes in the environment. Acknowledging the global robustness as an overly demanding requirement, we propose continuous implementa-tion as a local robustness of optimal mechanisms to small changes in the environment. We say that a social choice function is continuously implementable “with small trans-fers” if there exists a mechanism which yields the outcome close to the desired one for all types close to the designer’s initial model. We show that when a generic cor-relation condition is imposed on the class of interdependent values environments, any incentive compatible …

Random Mechanism Design On Multidimensional Domains, Shurojit Chatterji, Huaxia Zeng

Research Collection School Of Economics

We study random mechanism design in an environment where the set of alternatives has a Cartesian product structure. We first show that all generalized random dictatorships are strategy-proof on a minimally rich domain if and only if the domain is a top-separable domain. We next generalize the notion of connectedness (Monjardet, 2009) to establish a particular class of top-separable domains: connected domains, and show that in the class of minimally rich and connected domains, the multidimensional single-peakedness restriction is necessary and sufficient for the design of a flexible random social choice function that is unanimous and strategy-proof. Such a flexible …

Equivalence Of Stochastic And Deterministic Mechanisms, Yi-Chun Chen, Jiangtao Li, Jiangtao Li, Yeneng Sun

Research Collection School Of Economics

We consider a general social choice environment that has multiple agents, a finite set of alternatives, independent types, and atomless type distribution. We show that for any Bayesian incentive compatible mechanism, there exists an equivalent deterministic mechanism that (1) is Bayesian incentive compatible; (2) delivers the same interim expected allocation probabilities and the same interim expected utilities for all agents; and (3) delivers the same ex ante expected social surplus. This result holds in settings with a rich class of utility functions, multidimensional types, interdependent valuations, and in settings without monetary transfers. To prove our result, we develop a novel …

Limit Theory For Moderate Deviation From Integrated Garch Processes, Yubo Tao

Research Collection School Of Economics

This paper develops the limit theory of the GARCH(1,1) process that moderately deviates from IGARCH process towards both stationary and explosive regimes. The asymptotic theory extends Berkes et al. (2005) by allowing the parameters to have a slower rate of convergence. The results can be applied to unit root test for processes with mildly-integrated GARCH innovations (e.g. Boswijk (2001), Cavaliere and Taylor (2007, 2009)) and deriving limit theory of estimators for models involving mildly-integrated GARCH processes (e.g. Jensen and Rahbek (2004), Francq and Zakoïan (2012, 2013).

Wage-Vacancy Contracts And Multiplicity Of Equilibria In A Directed Search Model Of The Labor Market, Nicolas L. Jacquet, John Kennes, Serene Tan

Research Collection School Of Economics

This paper studies a directed search model of the labour market, which is standard in all aspects except two. First, we allow firms to post wage–vacancy contracts advertising the number of workers they would pay as well as the payment all will receive. Second, we consider two cases: one where workers are risk neutral and one where workers are risk averse, both in finite and large economies. Our paper shows that when firms post wage–vacancy contracts, whether workers are modelled as risk neutral or risk averse matters: the types of symmetric equilibria and the nature of multiplicity of equilibria are …

Three Essays On Nonstationary Time-Series Analysis And Network Dynamics, Yubo Tao

Dissertations and Theses Collection (Open Access)

My dissertation consists of three essays which contribute new theoretical results to nonstationary time-series analysis and network dynamics.

Chapter 2 examines the limit properties of information criteria (such as AIC, BIC, HQIC) for distinguishing between the unit root model and the various kinds of explosive models. The explosive models include the local-to-unit-root model, the mildly explosive model and the regular explosive model. Initial conditions with different orders of magnitude are considered. Both the OLS estimator and the indirect inference estimator are studied. It is found that BIC and HQIC, but not AIC, consistently select the unit root model when data …

Mixed Bayesian Implementation In General Environments, Takashi Kunimoto

Research Collection School Of Economics

A social choice rule is said to be mixed Bayesian implementable if one can design a mechanism (or institution) in which the set of all mixed Bayesian Nash equilibrium outcomes coincides with that specified by the rule. The objective of this paper is to generalize the results of mixed Bayesian implementation. By means of example, I first assess the implication of common priors in Bayesian implementation. Second, I identify a mild condition that fills the gap between the necessity and sufficiency for mixed Bayesian implementation in general environments including non-economic ones. Third, I establish some new results to unify the …

Equal-Quantile Rules In Resource Allocation With Uncertain Needs, Yan Long, Jay Sethuraman, Jingyi Xue

Research Collection School Of Economics

A group of agents have uncertain needs on a resource, and the resource has to be divided before uncertainty resolves. We propose a class of division rules we call equal-quantile rules, parameterized by λ ∈ (0, 1]. The parameter λ is a common maximal probability of satisfaction — the probability that an agent’s realized need is no more than his assignment — imposed on all agents. Thus, the maximal assignment of each agent is his λ-quantile assignment. If the endowment of the resource exceeds the sum of the agents’ λ-quantile assignments, each agent receives his λ-quantile assignment and the resource …

The Revealed Preference Theory Of Stable Matchings With One-Sided Preferences, Gaoji Hu, Jiangtao Li, Rui Tang

Research Collection School Of Economics

This note studies the testable implications of the theory of stable matchings intwo-sided matching markets with one-sided preferences. Our main result connects therevealed preference analysis to the well-known lattice structure of the set of stablematchings, and tests the rationalizability of a data set by analyzing the joins andmeets of matchings.

Robustly Optimal Reserve Price, Wei He, Jiangtao Li

Research Collection School Of Economics

We study a robust version of the single-unit auction problem. The auctioneer has confidence in her estimate of the marginal distribution of a generic bidder's valuation, but does not have reliable information about the joint distribution. In this setting, we analyze the performance of second-price auctions with reserve prices in terms of revenue guarantee, that is, the greatest lower bound of revenue across all joint distributions that are consistent with the marginals. For any finite number of bidders, we solve for the robustly optimal reserve price that generates the highest revenue guarantee. Our analysis has interesting implications in large markets. …

Maximum Likelihood Estimation For The Fractional Vasicek Model, Katsuto Tanaka, Weilin Xiao, Jun Yu

Research Collection School Of Economics

This paper is concerned about the problem of estimating the drift parameters in the fractional Vasicek model from a continuous record of observations. Based on the Girsanov theorem for the fractional Brownian motion, the maximum likelihood (ML) method is used. The asymptotic theory for the ML estimates (MLE) is established in the stationary case, the explosive case, and the null recurrent case for the entire range of the Hurst parameter, providing a complete treatment of asymptotic analysis. It is shown that changing the sign of the persistence parameter will change the asymptotic theory for the MLE, including the rate of …

Semiparametric Maximum Likelihood Inference For Nonignorable Nonresponse With Callbacks, Zhong Guan, Denis H. Y. Leung, Jing Qin

Research Collection School Of Economics

We model the nonresponse probabilities as logistic functions ofthe outcome variable and other covariates in the survey sampling study withcallback. The identification aspect of this callback model is investigated. Semiparametricmaximum likelihood estimators of the parameters in the responseprobabilities are proposed and studied. As a result, an efficient estimator ofthe mean of the outcome variable is constructed using the estimated responseprobabilities. Moreover, if a regression model for conditional mean of the outcomevariable given some covariate is available, then we can obtain an evenmore efficient estimate of the mean of the outcome variable by fitting the regressionmodel using an adjusted least squares …

Coarse Revealed Preference, Gaoji Hu, Jiangtao Li, John K. Quah, Rui Tang

Research Collection School Of Economics

We identify necessary and sufficient conditions under which a coarse data set canbe coarsely rationalized by a linear order (or weak order). The conditions are easy tocheck, and efficient algorithms are provided. We apply our theory to investigate theobservable restrictions of several economic models including (1) rational choice withimperfect observation; (2) multiple preferences; (3) monotone multiple preferences; and(4) minimax regret.

On Strategy-Proofness And The Salience Of Single-Peakedness, Shurojit Chatterji, Jordi Masso

Research Collection School Of Economics

We consider strategy-proof social choice functions operating on a rich domain of preference profiles. We show that if the social choice function satisfies in addition tops-onlyness, anonymity and unanimity then the preferences in the domain have to satisfy a variant of single-peakedness (referred to as semilattice single-peakedness). We do so by deriving from the social choice function an endogenous partial order (a semilattice) from which the notion of a semilattice single-peaked preference can be defined. We also provide a converse of this main finding. Finally, we show how well-known restricted domains under which nontrivial strategy-proof social choice functions are admissible …

Revisiting The Foundations Of Dominant-Strategy Mechanisms, Yi-Chun Chen, Jiangtao Li

Research Collection School Of Economics

An important question in mechanism design is whether there is any theoretical foundation for the use of dominant-strategy mechanisms. This paper studies the maxmin and Bayesian foundations of dominant-strategy mechanisms in general social choice environments with quasi-linear preferences and private values. We propose a condition called the uniform shortest-path tree that, under regularity, ensures the foundations of dominant-strategy mechanisms. This exposes the underlying logic of the existence of such foundations in the single-unit auction setting, and extends the argument to cases where it was hitherto unknown. To prove this result, we adopt the linear programming approach to mechanism design. In …

On Incentive Compatible, Individually Rational Public Good Provision Mechanisms, Takashi Kunimoto, Cuiling Zhang

Research Collection School Of Economics

This paper characterizes mechanisms satisfying Bayesian incentive compatibility (BIC) and interim individual rationality (IIR) in the classical public good provision problem. Many papers in the literature obtain the results in the so-called standard model of ex ante identical agents with a continuous, closed interval of types. Although the standard model and more generally a continuum type space are widely used in the literature, it is nonetheless an abstraction of reality. Given that the public good provision problem has occupied a central application in the theory of mechanism design, we propose a "stress test" for the results in the standard model …

Entrepreneurship, College, And Credit: The Golden Triangle, Roberto M. Samaniego, Juliana Yu Sun

Research Collection School Of Economics

We develop a model to evaluate the aggregate impact of college finance in an environment with entrepreneurship. The calibrated model captures the stylized fact that entrepreneurs with college are more common and more profitable in the United States. The calibration indicates this is mainly because higher labor earnings allow college‐educated agents to ameliorate credit constraints if and when they eventually become entrepreneurs. Changes in financing constraints on entrepreneurs can thus affect college attendance, and changes in financing constraints on college can affect entrepreneurship rates as well.