Probabilistic assignments of identical indivisible objects and uniform probabilistic rules

We consider a probabilistic approach to the problem of assigning k indivisible identical objects to a set of agents with single-peaked preferences. Using the ordinal extension of preferences we characterize the class of uniform probabilistic rules by Pareto efficiency, strategy-proofness, and no-envy. We also show that in this characterization no-envy cannot be replaced by anonymity. When agents are strictly risk averse von Neumann-Morgenstern utility maximizer, then we reduce the problem of assigning k identical objects to a problem of allocating the amount k of an infinitely divisible commodity.     

Platform market competition with endogenous side decisions

This paper develops a framework to analyze platform competition in two‐sided markets in which agents endogenously decide on which side of a platform to join. We characterize the equilibrium pricing structure and perform a comparative statics analysis on how the distribution of agents’ preferences affects the platforms’ profits. We also show that the market equilibrium under profit‐maximizing platforms leads to the first best social surplus, which illustrates the importance of the price mechanism to induce more balanced participation across the two sides. This framework can be applied to analyze market competition for “rental” or “sharing” platforms. In addition, we extend our analysis to consider an initial investment stage, which makes participants the owner of some durable goods to rent out.     

Ex-post favoring ranks: a fairness notion for the random assignment problem

We introduce two notions of ex-post fairness, namely ex-post favoring ranks (EFR) and robust ex-post favoring ranks, which consider whether objects are received by those agents who have the highest rank for them. We examine their compatibility with standard properties of random assignments and state some impossibility theorems. We also propose and formalize a revised version of the Boston mechanism and prove that it provides an EFR random assignment.

     

Additivity in minimum cost spanning tree problems

We characterize a rule in minimum cost spanning tree problems using an additivity property and some basic properties. If the set of possible agents has at least three agents, these basic properties are symmetry and separability. If the set of possible agents has two agents, we must add positivity.     

Mixed systems with minimal and maximal lifetime variances

We consider the mixed systems composed of a fixed number of components whose lifetimes are i.i.d. with a known distribution which has a positive and finite variance. We show that a certain of the k-out-of-n systems has the minimal lifetime variance, and the maximal one is attained by a mixture of series and parallel systems. The number of the k-out-of-n system, and the probability weights of the mixture depend on the first two moments of order statistics of the parent distribution of the component lifetimes. We also show methods of calculating extreme system lifetime variances under various restrictions on the system lifetime expectations, and vice versa.     

Is Stock Price Correlated with Oil Price? Spurious Regressions with Moderately Explosive Processes

This study explores the spurious effects in linear regressions with moderately explosive processes. Asymptotic results are developed for the least square estimator, the typical t‐statistic, the Durbin–Watson statistic, and the coefficient of determination. The typical t‐statistic is unable to detect the presence of a spurious relationship, due to the presence of nuisance parameters that characterize deviations from unity. Moreover, the t‐statistic for common explosive processes has different asymptotics compared to that for distinct explosive processes. Such differences further complicate the use of the t‐statistic. We demonstrate that two popular methods available in the literature are incapable for this purpose due to similar difficulties. To overcome these limitations, we propose a t‐test based upon balanced regressions that induces asymptotic inference based on the standard normal distribution, which is therefore robust to deviations from unity. These results are further generalized to spurious regressions with multivariate mildly explosive processes. Simulation results confirm that our test is effective in finite samples, while other alternatives are not. An empirical example that demonstrates the phenomenon of spurious correlation between the NASDAQ stock index and crude oil price in the US is provided to show the practical merit of our proposed method.     

On information-improvement and its generalization

TheTheil's information-improvement and its generalized form are consequences of different forms of the branching property that these measures are required to satisfy. We consider a seemingly more generalized form of the branching property and show that it does not lead to new measures. We also form a functional equation in three variables through this generalized branching property and show that this lead to the same result.The work is supported by a Post Doctoral Fellowship awarded to the author by Council of Scientific and Industrial Research, India.     

The Impact of Unrealized Fair Value Adjustments on Dividend Policy

We examine the impact of unrealized fair value adjustments on dividend policy. Dividend payouts should include only persistent income [Lintner, J. (1956). Distribution of incomes of corporations among dividends, retained earnings and taxes. American Economic Review, 46(2), 97–113]. In our institutional setting, however, regulators recommend the non-distribution of any income from fair value adjustments, which suggests that they interpret them as transitory. We empirically demonstrate that fair value adjustments on investment property are persistent, while those on financial securities are transitory. We further show that only fair value adjustments from investment properties are distributed. We argue that managers perceive the persistence of the two fair value components correctly, and by doing so, they distribute income consistent with the Lintner framework rather than on regulatory recommendations. Finally, by focusing on managerial optimism, debt contracting, and insider ownership, we demonstrate the conditions under which firms choose to deviate from regulator recommendations and to distribute fair value profits.     

Peer‐to‐Peer File Sharing and the Market for Digital Information Goods

We study competitive interaction between two alternative models of digital content distribution over the Internet: peer‐to‐peer (p2p) file sharing and centralized client–server distribution. We present microfoundations for a stylized model of p2p file sharing where all peers are endowed with standard preferences and show that the endogenous structure of the network is conducive to sharing by a significant number of peers, even if sharing is costlier than freeriding. We build on this model of p2p to analyze the optimal strategy of a profit‐maximizing firm, such as Apple, that offers content available at positive prices. We characterize the size of the p2p network as a function of the firm's pricing strategy, and show that the firm may be better off setting high prices, allowing the network to survive, and that the p2p network may work more efficiently in the presence of the firm than in its absence.     

Survival and the art of profit maximization

We study the relationship between rationality and economic survival in a simple dynamic model, where agents from different populations interact repeatedly through random matching. An explicit criterion (“bankruptcy”) determines whether agents survive each interaction; all agents are presumed to be aware of this criterion. Survival in each interaction depends on two factors: the strategies agents adopt when they interact, and the wealth levels they bring to the game. The model is completely symmetric with the only difference between the agents of different populations being their objectives. We consider the case where there are two populations of agents in which all agents from one group have as their objective, maximizing the expected profits from each interaction, while all agents from the other attempt simply to maximize the probability of surviving (i.e., not going bankrupt in) the interaction. We show that under the equilibrium dynamics, the proportions of each group in the total population must be bounded away from zero, but the balance is in favor of the survival-probability maximizers in that their numbers as a fraction of total population must always exceed 1/2, and can be arbitrarily close to unity. On the other hand, the fraction of total wealth controlled by the expected profit maximizers must also be at least 1/2, and can asymptotically tend to unity.     

Model selection with estimated factors and idiosyncratic components

This paper provides consistent information criteria for the selection of forecasting models that use a subset of both the idiosyncratic and common factor components of a big dataset. This hybrid model approach has been explored by recent empirical studies to relax the strictness of pure factor‐augmented model approximations, but no formal model selection procedures have been developed. The main difference to previous factor‐augmented model selection procedures is that we must account for estimation error in the idiosyncratic component as well as the factors. Our main contribution is to show the conditions required for selection consistency of a class of information criteria that reflect this additional source of estimation error. We show that existing factor‐augmented model selection criteria are inconsistent in circumstances where N is of larger order than , where N and T are the cross‐section and time series dimensions of the dataset respectively, and that the standard Bayesian information criterion is inconsistent regardless of the relationship between N and T. We therefore propose a new set of information criteria that guarantee selection consistency in the presence of estimated idiosyncratic components. The properties of these new criteria are explored through a Monte Carlo simulation study. The paper concludes with an empirical application to long‐horizon exchange rate forecasting using a recently proposed model with country‐specific idiosyncratic components from a panel of global exchange rates.     

A study on the mean past lifetime of the components of (n − k + 1)-out-of-n system at the system level

In the present paper, we consider a (n − k + 1)-out-of-n system with identical components where it is assumed that the lifetimes of the components are independent and have a common distribution function F. We assume that the system fails at time t or sometime before t, t > 0. Under these conditions, we are interested in the study of the mean time elapsed since the failure of the components. We call this as the mean past lifetime (MPL) of the components at the system level. Several properties of the MPL are studied. It is proved that the relation between the proposed MPL and the underlying distribution is one-to-one. We have shown that when the components of the system have decreasing reversed hazard then the MPL of the system is increasing with respect to time. Some examples are also provided.     

On the Choice of Risk and Effort in Tournaments—Experimental Evidence

We investigate a simple two‐person tournament in a controlled laboratory experiment. Each player chooses between two distributions of random shocks. After observing the overall risk, both players decide simultaneously on their effort. Theory predicts both players should choose the distribution with the higher variance of random shock, as this minimizes equilibrium effort. We show that the effort exerted is sensitive towards risk. The agents exert less effort if the random shock is high. However, agents do not learn to commit themselves by choosing a high risk in our experiment.     

Limiting Dictatorial rules

We consider the preference aggregation problem in infinite societies. In our model, there are arbitrarily many agents and alternatives, and admissible coalitions may be restricted to lie in an algebra. In this framework (which includes the standard one), we characterize, in terms of Strict Neutrality, the Ultrafilter Property of preference aggregation rules. Based on this property, we define the concept of Limiting Dictatorial rules, which are characterized by the existence of arbitrarily small decisive coalitions. We show that, in infinite societies which can be well approximated by finite ones, any Arrovian rule is limiting.     

Forensic identification: the island problem and its generalisations

In forensics it is a classical problem to determine, when a suspect S shares a property Γ with a criminal C, the probability that S = C. In this article we give a detailed account of this problem in various degrees of generality. We start with the classical case where the probability of having Γ, as well as the a priori probability of being the criminal, is the same for all individuals. We then generalize the solution to deal with heterogeneous populations, biased search procedures for the suspect, Γ‐correlations, uncertainty about the subpopulation of the criminal and the suspect, and uncertainty about theΓ‐frequencies. We also consider the effect of the way the search for S is conducted, in particular when this is done by a database search. A returning theme is that we show that conditioning is of importance when one wants to quantify the ‘weight’ of the evidence by a likelihood ratio. Apart from these mathematical issues, we also discuss the practical problems in applying these issues to the legal process. The posterior probabilities of C = S are typically the same for all reasonable choices of the hypotheses, but this is not the whole story. The legal process might force one to dismiss certain hypotheses, for instance when the relevant likelihood ratio depends on prior probabilities. We discuss this and related issues as well. As such, the article is relevant both from a theoretical and from an applied point of view.     

Multiple equilibria in two-sector monetary economies: An interplay between preferences and the timing for money

In this paper, we study the occurrence of local indeterminacy in two-sector monetary economies. We consider a general MIUF model with two alternative timings in monetary payments: the Cash-In-Advance timing, in which the cash available to buy goods is money in the consumers’ hands after they leave the bond market but before they enter the goods market, and the Cash-After-the-Market timing, in which agents hold money for transactions after leaving the goods market. We consider three standard specifications of preferences: the additively separable formulation, the Greenwood–Hercovitz–Huffman (GHH) (Greenwood et al., 1988) formulation and the King–Plosser–Rebelo (KPR) (King et al., 1988) formulation. First, we show that for all the three types of preferences, local indeterminacy occurs under the CIA timing with a low enough interest rate elasticity of money demand. Second, we show that with the CAM timing, although determinacy always holds under separable preferences, local indeterminacy can occur with GHH and KPR preferences. We thus prove that compared to aggregate models, two-sector models provide new rooms for local indeterminacy when non-separable standard preferences are considered.     

Bounds for the mean residual life function of a <Emphasis Type="Italic">k</Emphasis>-out-of-<Emphasis Type="Italic">n</Emphasis> system

In the reliability studies, k-out-of-n systems play an important role. In this paper, we consider sharp bounds for the mean residual life function of a k-out-of-n system consisting of n identical components with independent lifetimes having a common distribution function F, measured in location and scale units of the residual life random variable X _t  = (X−t|X > t). We characterize the probability distributions for which the bounds are attained. We also evaluate the so obtained bounds numerically for various choices of k and n.     

Tests of Policy Interventions in DSGE Models

This paper considers tests of the effectiveness of a policy intervention, defined as a change in the parameters of a policy rule, in the context of a macroeconometric dynamic stochastic general equilibrium (DSGE) model. We consider two types of intervention, first the standard case of a parameter change that does not alter the steady state, and second one that does alter the steady state, e.g. the target rate of inflation. We consider two types of test, one a multi‐horizon test, where the postintervention policy horizon, H, is small and fixed, and a mean policy effect test where H is allowed to increase without bounds. The multi‐horizon test requires Gaussian errors, but the mean policy effect test does not. It is shown that neither of these two tests are consistent, in the sense that the power of the tests does not tend to unity as H→∞, unless the intervention alters the steady state. This follows directly from the fact that DSGE variables are measured as deviations from the steady state, and the effects of policy change on target variables decay exponentially fast. We investigate the size and power of the proposed mean effect test by simulating a standard three equation New Keynesian DSGE model. The simulation results are in line with our theoretical findings and show that in all applications the tests have the correct size; but unless the intervention alters the steady state, their power does not go to unity with H.     

Partnership-enhancement and stability in matching problems

In two-sided matching problems, we consider “natural” changes in preferences of agents in which only the rankings of current partners are enhanced. We introduce two desirable properties of matching rules under such rank-enhancements of partners. One property requires that an agent who becomes higher ranked by the original partner should not be punished. We show that this property cannot always be met if the matchings are required to be stable. However, if only one agent changes his preferences, the above requirement is compatible with stability, and moreover, envy-minimization in stable matchings can also be attained. The other property is a solidarity property, requiring that all of the “irrelevant” agents, whose preferences as well as whose original partners’ preferences are unchanged, should be affected in the same way; either all weakly better off or all worse off. We show that when matchings are required to be stable, this property does not always hold.     

Consistency in the probabilistic assignment model

This paper introduces a notion of consistency for the probabilistic assignment model, which we call probabilistic consistency. We show that the axioms equal treatment of equals and probabilistic consistency characterize the uniform rule, which is the rule which randomizes uniformly over all possible assignments.