Economic Theory Commons^™

Are Tournaments Optimal Over Piece Rates Under Limited Liability For The Principal?, Kosmas Marinakis, Theofanis Tsoulouhas

Research Collection School Of Economics

A highly acclaimed result is that tournaments are superior to piece rates when the agents are risk averse and their production activities are subject to a relatively large common shock. The reason is that tournaments allow the principal to trade insurance for lower income to the agents. Our analysis shows that this celebrated result does not carry over to the case when a limited liability (bankruptcy) constraint limits the payments the principal can make, provided that the liquidation value of the firm is sufficiently small. This finding has important implications for the vast number of limited liability firms. Even though …

On Domains That Admit Well-Behaved Strategy-Proof Social Choice Functions, Shurojit Chatterji, Rezmi Sanver, Arunava Sen

Research Collection School Of Economics

In this paper, we investigate domains that admit “well-behaved” strategy-proof social choice functions. We show that if the number of voters is even, then every domain that satisfies a richness condition and admits an anonymous, tops-only, unanimous and strategy-proof social choice function, must be semi-single-peaked. Conversely every semi-single-peaked domain admits an anonymous, tops-only, unanimous and strategy-proof social choice function. Semi-single-peaked domains are generalizations of single-peaked domains on a tree introduced by Demange (1982).

A Smooth Test For The Equality Of Distributions, Anil Bera, Aurobindo Ghosh, Zhijie Xiao

Research Collection School Of Economics

The two-sample version of the celebrated Pearson goodness-of-fit problem has been a topic of extensive research, and several tests like the Kolmogorov-Smirnov and Cramer-von Mises have been suggested. Although these tests perform fairly well ´ as omnibus tests for comparing two probability density functions (PDFs), they may have poor power against specific departures such as in location, scale, skewness, and kurtosis. We propose a new test for the equality of two PDFs based on a modified version of the Neyman smooth test using empirical distribution functions minimizing size distortion in finite samples. The suggested test can detect the specific directions …

Robust Virtual Implementation: Toward A Reinterpretation Of The Wilson Doctrine, Georgy Artemov, Takashi Kunimoto, Roberto Serrano

Research Collection School Of Economics

We study a mechanism design problem where arbitrary restrictions are placed on the sets of first-order beliefs of agents. Calling these restrictions Δ, we use Δ-rationalizability (Battigalli and Siniscalchi, 2003, [5]) as our solution concept, and require that a mechanism virtually implement a socially desirable outcome. We obtain two necessary conditions, Δ-incentive compatibility and Δ-measurability and show that the latter is satisfied as long as a particular zero-measure set of first-order beliefs is ruled out. In environments allowing small transfers of utility among agents, these two conditions are also sufficient.

Optimal City Hierarchy: A Dynamic Programming Approach To Central Place Theory, Wen-Tai Hsu, Thomas J. Holmes, Frank Morgan

Research Collection School Of Economics

Central place theory is a key building block of economic geography and an empirically plausible description of city systems. This paper provides a rationale for central place theory via a dynamic programming formulation of the social planner's problem of city hierarchy. We show that there must be one and only one immediate smaller city between two neighboring larger-sized cities in any optimal solution. If the fixed cost of setting up a city is a power function, then the immediate smaller city will be located in the middle, confirming the locational pattern suggested by Christaller [4] . We also show that …

The Structure Of Strategy-Proof Random Social Choice Functions Over Product Domains And Lexicographically Separable Preferences, Shurojit Chatterji, Souvik Roy, Arunava Sen

Research Collection School Of Economics

We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for …

Contracting Over Prices, Shurojit Chatterji, Sayantan Ghosal

Research Collection School Of Economics

We define a solution concept, perfectly contracted equilibrium, for an intertemporal exchange economy where agents are simultaneously price takers in spot commodity markets while engaging inefficient, non-Walrasian contracting over future prices. Without requiring that agents have perfect foresight, we show that perfectly contracted equilibrium outcomes are a subset of Pareto optimal allocations. It is a robust possibility for perfectly contracted equilibrium outcomes to differ from Arrow-Debreu equilibrium outcomes. We show that both centralized banking and retrading with bilateral contracting can lead to perfectly contracted equilibria.

Subgame Perfect Implementation Under Information Perturbations, Takashi Kunimoto, Drew Fudenberg, Takashi Kunimoto, Oliver Tercieux

Research Collection School Of Economics

We consider the robustness of extensive form mechanisms to deviations from common knowledge about the state of nature, which we refer to as information perturbations. First, we show that even under arbitrarily small information perturbations the Moore-Repullo mechanism does not yield (even approximately) truthful revelation and that in addition the mechanism has sequential equilibria with undesirable outcomes. More generally, we prove that any extensive form mechanism is fragile in the sense that if a non-Maskin monotonic social objective can be implemented with this mechanism, then there are arbitrarily small information perturbations under which an undesirable sequential equilibrium also exists. Finally, …

Unilateral Measures And Emissions Mitigation, Shurojit Chatterji, Sayantan Ghosal, Sean Walsh, John Whalley

Research Collection School Of Economics

We discuss global climate mitigation that builds on existing unilateral measures to cut emissions. We document and discuss the rationale for such unilateral measures argue that such measures have the potential to generate positive spillover effects both within and across countries. In a simple dynamic model of learning we show that while single countries on their own may never get to the point of switching completely to low emission activities, a learning process with positive spillovers across nations is more likely to deliver a global switch to low emissions. We discuss the key features of a new global Intellectual Property …

A Generalized Representation Theorem For Harsanyi's ('Impartial') Observer, Simon Grant, Atsushi Kajii, Ben Polak, Zvi Safra

Research Collection School Of Economics

We provide an axiomatization of an additively separable social welfare function in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's setting to make the lotteries over the identities the observer may assume independent of the social alternative.

Inefficiency In The Shadow Of Unobservable Outside Options, Madhav S. Aney

Research Collection School Of Economics

This paper considers the problem of allocating an object between two players in an environment with one sided asymmetric information when their outside options depend on each other's type, causing the outside option of the uninformed player to be unobservable to her. Consequently efficient mechanisms under budget balance are not always available even when there is no uncertainty about which of the two players values the object more. A simple condition on the outside options turns out to be both necessary and sufficient to guarantee the first best. I also characterise the second best allocation under some conditions and show …

Random Dictatorship Domains, Shurojit Chatterji, Arunava Sen, Huaxia Zeng

Research Collection School Of Economics

A domain of preference orderings is a random dictatorship domain if every strategy- proof random social choice function satisfying unanimity defined on the domain, is a random dictatorship. Gibbard (1977) showed that the universal domain is a random dictatorship domain. We investigate the relationship between dictatorial and random dictatorship domains. We show that there exist dictatorial domains that are not random dictatorship domains. We provide stronger versions of the linked domain condition (introduced in Aswal et al. (2003)) that guarantee that a domain is a random dictatorship domain. A key step in these arguments that is of independent interest, is …

Nonlinear Cointegrating Regression Under Weak Identification, Xiaoxia Shi, Peter C. B. Phillips

Research Collection School Of Economics

An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the finite-sample distributions of nonlinear least squares estimators, resulting in potentially misleading inference. A new local limit theory is developed that approximates the finite-sample distributions of the estimators uniformly well irrespective of the strength of the identification. An important technical component of …

Testing For Jumps In Noisy High Frequency Data, Yacine Ait-Sahalia, Jean Jacod, Jia Li

Research Collection School Of Economics

This paper proposes a robustification of the test statistic of Aït-Sahalia and Jacod (2009b) for the presence of market microstructure noise in high frequency data, based on the pre-averaging method of Jacod et al. (2010). We show that the robustified statistic restores the test's discriminating power between jumps and no jumps despite the presence of market microstructure noise in the data.

Wage-Vacancy Contracts And Coordination Frictions, Nicolas L. Jacquet, Serene Tan

Research Collection School Of Economics

We consider a directed search model with risk-averse workers and risk-neutral entrepreneurs who can set up firms that post wage-vacancy contracts, i.e., contracts where firms can make payments to more than one applicant, and where the payments can be different for each applicant and be contingent on the number of applicants. We establish that the type of contracts the literature focuses on are not offered if firms can post wage-vacancy contracts. We show that there exists an equilibrium satisfying a Monotonic Expected Utility property which is efficient. Furthermore, we investigate the role of wage-vacancy contracts on welfare and competition.

A Comparison Of Cardinal Tournaments And Piece Rate Contracts With Liquidity Constrained Agents, Kosmas Marinakis, Theofanis Tsoulouhas

Research Collection School Of Economics

Acelebrated result in the theory of tournaments is that relative performance evaluation (tournaments) is a superior compensation method to absolute performance evaluation (piece rate contracts) when the agents are risk-averse, the principal is risk-neutral or less risk-averse than the agents and production is subject to common shocks that are large relative to the idiosyncratic shocks. This is because tournaments get closer to the first best by filtering common uncertainty. This paper shows that, surprisingly, tournaments are superior even when agents are liquidity constrained so that transfers to them cannot fall short of a predetermined level. The rationale is that, by …

Single Peakedness And Giffen Demand, Massimiliano Landi

Research Collection School Of Economics

I provide a simple example of a single peaked utility function that generates a Giffen demand. The utility function is smooth, non piecewise defined, strictly concave but not globally increasing. A full characterization of the parameter conditions under which the Giffen demand arises is provided. In addition the properties of the demand function are studied: I find that the inferior commodity with a Giffen demand must be cheaper relatively to a substitute and that Giffen demand arises at relatively low levels of income. However it is not required that the share of income spent on that commodity be large.

Power Maximization And Size Control Of Heteroscedasticity And Autocorrelation Robust Tests With Exponentiated Kernels, Yixiao Sun, Peter C. B. Phillips, Sainan Jin

Research Collection School Of Economics

Using the power kernels of Phillips, Sun, and Jin (2006, 2007), we examine the large sample asymptotic properties of the t-test for different choices of power parameter (ρ). We show that the nonstandard fixed-ρ limit distributions of the t-statistic provide more accurate approximations to the finite sample distributions than the conventional large-ρ limit distribution. We prove that the second-order corrected critical value based on an asymptotic expansion of the nonstandard limit distribution is also second-order correct under the large-ρ asymptotics. As a further contribution, we propose a new practical procedure for selecting the test-optimal power parameter that addresses the central …

A New Necessary Condition For Implementation In Iteratively Undominated Strategies, Takashi Kunimoto, Roberto Serrano

Research Collection School Of Economics

We uncover a new necessary condition for implementation in iteratively undominated strategies by mechanisms that satisfy the “best element property” where for each agent, there exists a strategy profile that gives him the highest payoff in the mechanism. This class includes finite and regular mechanisms. We conclude that either the quasilinearity-like assumptions of available sufficiency results cannot be completely dispensed with or some mechanisms that do not satisfy the best element property must be employed. We term the condition “restricted deception-proofness.” It requires that, in environments with identical preferences, the social choice function be immune to all deceptions, making it …

Predictions For Protection: A System To Measure And Detect Asset Bubbles, Singapore Management University

Perspectives@SMU

The damage wrecked by the bursting of asset bubbles can have a devastating impact on investors' fortunes. In the Internet bubble, some US$8 trillion of shareholder wealth was destroyed. What is even more pertinent, however, is how the popping of a bubble can create a financial crisis, impacting nations and their economies. As a result, understanding how to identify bubbles is an important first step in combating these speculative bubbles, with interested parties ranging from the academic and investment community to central bankers and policy makers.

Tops-Only Domains, Shurojit Chatterji, Arunava Sen

Research Collection School Of Economics

In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question: what are the characteristics of domains D" role="presentation">D that induce the property that every strategy-proof social choice function f:Dn→A" role="presentation">f:Dn→A satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on D" role="presentation">D that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n …

Tops-Only Domains, Shurojit Chatterji, Arunava Sen

Research Collection School Of Economics

In this paper we consider the standard voting model with a finite set of alternativesA and n voters and address the following question: what are the characteristics ofdomains D that induce the property that every strategy-proof social choice functionf : Dn → A satisfying unanimity, has the tops-only property? We first impose aminimal richness condition which ensures that for every alternative a, there exists anadmissible ordering where a is maximal. We identify conditions on D that are sufficientfor strategy-proofness and unanimity to imply tops onlyness in the general case of nvoters and in the special case, n = 2. We …

Corrigendum To "A Gaussian Approach For Continuous Time Models Of The Short Term Interest Rate", Peter C. B. Phillips, Jun Yu

Research Collection School Of Economics

An error is corrected in Yu and Phillips (2001) (Econometrics Journal, 4, 210-224) where a time transformation was used to induce Gaussian disturbances in the discrete time equivalent model. It is shown that the error process in this model is not a martingale and the Dambis, Dubins-Schwarz (DDS) theorem is not directly applicable. However, a detrended error process is a martingale, the DDS theorem is applicable, and the corresponding stopping time correctly induces Gaussianity. We show that the two stopping time sequences differ by O(a2), where a is the pre-specified normalized timing constant.

A Sufficient Condition For The Tops-Only Property Of Strategy-Proof Social Choice Functions In The Case Of Two Voters, Huaxia Zeng

Dissertations and Theses Collection (Open Access)

In this thesis, we consider the standard voting model with a finite set of alternatives A and 2 voters, and address the following question: besides Domains D satisfying the

Property T (Chatterji & Sen (2011) ), what are other characteristics of domains that induce every strategy-proof and unanimous social choice function f : Dn → A to satisfy the tops-only property? We impose a minimal richness condition which ensures that for every alternative a ∈ A, there exists a preference ordering where a is maximal. We identify a more general condition on domains that is sufficient for strategy-proofness …

Simulation-Based Estimation Methods For Financial Time Series Models, Jun Yu

Research Collection School Of Economics

This paper overviews some recent advances on simulatio n-based methods of estimating time series models and asset pricing models that are widely used in finance. The simulation based methods have proven to be particularly useful when the likelihood function and moments do not have tractable forms and hence the maximum likelihood method (MLE) and the generalized method of moments (GMM) are difficult to use. They can also be useful for improving the finite sample performance of the traditional methods when financial time series are highly persistent and when the quantity of interest is a highly nonlinear function of system parameters.The …

A New Bayesian Unit Root Test In Stochastic Volatility Models, Yong Li, Jun Yu

Research Collection School Of Economics

A new posterior odds analysis is proposed to test for a unit root in volatility dynamics in the context of stochastic volatility models. This analysis extends the Bayesian unit root test of So and Li (1999, Journal of Business Economic Statistics) in two important ways. First, a numerically more stable algorithm is introduced to compute the Bayes factor, taking into account the special structure of the competing models. Owing to its numerical stability, the algorithm overcomes the problem of diverged “size” in the marginal likelihood approach. Second, to improve the “power” of the unit root test, a mixed prior specification …

Indescribability And Its Irrelevance For Contractual Incompleteness, Takashi Kunimoto

Research Collection School Of Economics

The incomplete contracts literature often cites indescribable contingencies as a major obstacle to the creation of completecontracts. Using agents’ minimum foresight concerning possible future payoffs, Maskin and Tirole (Rev Econ Stud 66:83–114, 1999) show that indescribability does not matter for contractual incompletenessas long as there is symmetric information at both the contracting stage and the trading stage. This is called the irrelevance theorem. The following generalization of the irrelevance theorem is shown here: indescribability does not matter even in the presenceof asymmetric information at the trading stage, as long as there is symmetric information at the contracting stage. This isan …

Evaluating The Conditions For Robust Mechanism Design, Takashi Kunimoto, Roberto Serrano

Research Collection School Of Economics

We assess the strength of the different conditions identified in the literature of robustmechanism design. We focus on three conditions: ex post incentive compatibility,robust monotonicity, and robust measurability. Ex post incentive compatibility hasbeen shown to be necessary for any concept of robust implementation, while robustmonotonicity and robust measurability have been shown to be necessary for robust(full) exact and virtual implementation, respectively. This paper shows that whileviolations of ex post incentive compatibility and robust monotonicity do not easily goaway, we identify a mild condition on environments in which robust measurability issatisfied by all social choice functions over a residual set (i.e., …

How Robust Is Undominated Nash Implementation?, Takashi Kunimoto

Research Collection School Of Economics

Palfrey and Srivastava (1991) show that almost any social choice correspondence(SCC) is implemented in undominated Nash equilibrium, a refinement of Nash equilibrium. By requiring solution concepts to have closed graph in the limit of complete information, Chung and Ely (2003) investigate the robustness of undominated Nash implementation. Their robustness test concludes that when preferences are strict (or more generally, hedonic), only monotonic SCCs can be implemented in the closure of the undominated Nash (equilibrium) correspondence. This paper re-examines this robustness test. I show that almost any SCC is implemented in the closure of the undominated Nash correspondence, provided that the …

Unilateral Measures And Emissions Mitigation, Shurojit Chatterji, Sayantan Ghosal, Sean Walsh, John Whalley

Research Collection School Of Economics

We discuss global climate mitigation that builds on existing unilateral measures to cut emissions. We document and discuss the rationale for such unilateral measures argue that such measures have the potential to generate positive spillover effects both within and across countries. In a simple dynamic model of learning we show that while single countries on their own may never get to the point of switching completely to low emission activities, a learning process with positive spillovers across nations is more likely to deliver a global switch to low emissions. We discuss the key features of a new global Intellectual Property …