Stepwise Bayes distributional inference for a finite population

Stepwise Bayes arguments can be used to derive various decision rules. Admissibility of such rules follows if additional conditions are satisfied. We show that in complete generality almost admissibility is in place. A uniform distribution example is used to demonstrate how stepwise Bayes arguments can be used when the support of the observation distribution depends on the unknown parameter. We then discuss distributional inference and show that weighted Polya posterior distributions provide admissible distributional inference for finite population problems when strictly proper loss functions are used.     

A primal Divisia technical change index based on the output distance function

We derive a primal Divisia technical change index based on the output distance function and further show the validity of this index from both economic and axiomatic points of view. In particular, we derive the primal Divisia technical change index by total differentiation of the output distance function with respect to a time trend. We then show that this index is dual to the Jorgenson and Griliches (1967) dual Divisia total factor productivity growth (TFPG) index when both the output and input markets are competitive; dual to the Diewert and Fox (2008) markup-adjusted revenue-share-based dual Divisia technical change index when market power is limited to output markets; dual to the Denny et al. (1981) and Fuss (1994) cost-elasticity-share-based dual Divisia TFPG index when market power is limited to output markets and constant returns to scale is present; and also dual to a markup-and-markdown-adjusted Divisia technical change index when market power is present in both output and input markets. Finally, we show that the primal Divisia technical change index satisfies the properties of identity, commensurability, monotonicity, and time reversal. It also satisfies the property of proportionality in the presence of path independence, which in turn requires separability between inputs and outputs and homogeneity of subaggregator functions.     

Learning and coordination with dispersed information

We analyse adaptive learning in a model of incomplete and dispersed information, with externalities and strategic interactions. We build on the framework proposed by Angeletos and Pavan (2007a) and extend it to a dynamic multi-period setting where agents need to learn to coordinate. We derive conditions under which adaptive learning obtains in such setting and show that, when actions are strategic substitutes, the information structure affects the speed of convergence: while more precise private information is beneficial, better public information has negative effects. We also show that adaptive learning dynamics converge to the Bayesian Nash equilibrium, which means that agents can learn to act strategically by relying only on observable (exogenous) information.     

A note on Musgrave asymmetrical trend-cycle filters

In this paper, we derive the implicit forecasts in the asymmetrical trend-cycle averages used in the X-11 seasonal adjustment method. We give an algorithm to calculate them, and we study their statistical properties. We express the forecasts as Stein estimators. We derive expressions for their bias, variance, covariances and prediction mean squared errors. We show that the prediction mean squared errors of the implied predictors are always smaller or equal to those obtained using the least squares predictors. Finally, we derive the prior distributions under which the implied predictors are Bayes estimators.     

Consuming durable goods when stock markets jump: A strategic asset allocation approach

In this paper we show the impact of considering jumps in the return process of risky assets when deciding how to invest and consume throughout time. Agents derive their utilities from consumption over time. We consider an agent that invests in the financial market and in durable and perishable consumption goods. Assuming that there are costs for transacting the durable good, we show that an agent who does not consider the possibility of jumps will make suboptimal decisions, not only regarding the fraction of wealth invested in the stock market, but also with respect to the timing for trading on the durable good. Furthermore we also show that jumps cause a non-obvious asymmetric impact on the thresholds that lead the consumer to trade the durable good, even when the jump distribution is symmetric.     

Spatial differentiation,divisible consumption and the pro-competitive effect of income

We analyze a spatial differentiation model with divisible consumption under one-stop shopping. Each consumer who visits only one store, chooses the quantities of the goods which maximize his/her utility function under the budget constraint (namely consumption expenditures must equal income minus transportation costs), choosing the store which provides him/her with the largest indirect utility. We derive the equilibrium price when the firms are located at the two extremities of Hotelling’s linear city and show that income increases have a pro-competitive effect.     

Implementation with partial verification

This paper examines the implementability of social choice functions when only partial verification of private information is possible. Green and Laffont (1986) used this framework to derive a necessary and sufficient condition for the revelation principle to continue to hold with partial verification. We provide economically interesting characterizations of this condition, which suggest that it may be too restrictive. This leads us to consider implementation (not necessarily truthful) in general, when there is partial verification. We consider the case where compensatory transfers are allowed, giving the mechanism designer further leeway. We show how partial verification may allow efficient implementation of bilateral trade, where it would otherwise not be possible. Received: 1 August 1998 / Accepted: 5 September 2000     

Bayesian quantile regression methods

This paper is a study of the application of Bayesian exponentially tilted empirical likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys' method. For regression quantiles we derive the asymptotic form of the posterior density. We also examine Markov chain Monte Carlo simulations with a proposal density formed from an overdispersed version of the limiting normal density. We show that the algorithm works well even in models with an endogenous regressor when the instruments are not too weak. Copyright © 2009 John Wiley & Sons, Ltd.     

Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations

Phenomena such as the Great Moderation have increased the attention of macroeconomists towards models where shock processes are not (log-)normal. This paper studies a class of discrete-time rational expectations models where the variance of exogenous innovations is subject to stochastic regime shifts. We first show that, up to a second-order approximation using perturbation methods, regime switching in the variances has an impact only on the intercept coefficients of the decision rules. We then demonstrate how to derive the exact model likelihood for the second-order approximation of the solution when there are as many shocks as observable variables. We illustrate the applicability of the proposed solution and estimation methods in the case of a small DSGE model.     

Index

We study two Durbin-Watson type tests for serial correlation of errors inregression models when observations are missing. We derive them by applying standard methods used in time series and linear models to deal with missing observations. The first test may be viewed as a regular Durbin-Watson test in the context of an extended model. We discuss appropriate adjustments that allow one to use all available bounds tables. We show that the test is locally most powerful invariant against the same alternative error distribution as the Durbin-Watson test. The second test is based on a modified Durbin-Watson statistic suggested by King (1981a) and is locally most powerful invariant against a first-order autoregressive process.     

Value-at-Risk under Measurement Error

We propose a method for estimating Value-at-Risk that corrects for the effect of measurement errors in stock prices. We show that the presence of measurement errors might pose serious problems for estimating risk measures. In particular, when stock prices are contaminated, existing estimators of Value-at-Risk are inconsistent and might lead to an underestimation of risk, which can result in extreme leverage ratios within the held portfolios. Using a Fourier transform and a deconvolution kernel estimator of the probability distribution function of actual latent prices, we derive a robust estimator of Value-at-Risk in the presence of measurement errors. Monte Carlo simulations and real data analysis illustrate satisfactory performance of the proposed method.     

SMEs and public procurement policy

In this paper, we characterize an optimal procurement policy as a mechanism design problem when an allotment of the contract is available, i.e., when a government faces both SMEs and large firms for carrying out a heterogeneously divisible project. Our model allows us to analyze all procurement policies (set-asides, favoritism, non-discriminatory rules), taking into account both efficiency and distributive arguments and derive a normative framework. We show that set-asides are not generally optimal, whatever the industrial preferences of the government are, while the optimal preferential treatments of firms implies complex non-linear rules. We prove that the optimal policy can be implemented using a modified Vickrey-type auction. We also consider that the firms can reduce their cost by a non observable effort, and exhibit the specific impact of cost reduction incentives on the optimal policies.Received: 24 September 2001, JEL Classification: D44Pierre-HenriMorand : I am grateful to the anonymous referees for comments. The usualdisclaimer applies.     

Testing cointegration relationship in a semiparametric varying coefficient model

In this paper, we develop two cointegration tests for two varying coefficient cointegration regression models, respectively. Our test statistics are residual based. We derive the asymptotic distributions of test statistics under the null hypothesis of cointegration and show that they are consistent against the alternative hypotheses. We also propose a wild bootstrap procedure companioned with the continuous moving block bootstrap method proposed in  Paparoditis and Politis (2001) and  Phillips (2010) to rectify severe distortions found in simulations when the sample size is small. We apply the proposed test statistic to examine the purchasing power parity (PPP) hypothesis between the US and Canada. In contrast to the existing results from linear cointegration tests, our varying coefficient cointegration test does not reject that PPP holds between the US and Canada.     

Valuation of piecewise linear barrier options

This paper discusses the valuation of piecewise linear barrier options that generalize classical barrier options. We establish formulas for joint probabilities of the logarithmic returns of the underlying asset and its partial running maxima when the process has a piecewise constant drift. In particular, we show that our results embrace the famous reflection principle as a special case, and that our established proposition delivers useful scalability for computing desired probabilities related to various types of barriers. We derive the closed-form prices of piecewise linear barrier options under the Black–Scholes framework, which are obtainable with little effort by relying on the derived probabilities. In addition, we provide numerical examples and discuss how option prices respond to several types of piecewise linear barriers.     

Distressed exchange,bargaining power,and prior capital structure

Financially troubled companies often make Distressed Exchange (DE) offers to its creditors, to postpone costly bankruptcy reorganization. We derive the optimal terms and timing of a DE offer consisting of debt reduction and an equity stake in the restructured firm. The DE terms and timing are affected by shareholder bargaining power, with greater shareholder bargaining power resulting in earlier DE offer, smaller debt reduction and smaller equity stake. The impact of shareholder bargaining power is greater when bankruptcy cost is larger and tax rate is higher. We also show that renegotiability of debt increases ex-ante firm value and results in a higher optimal leverage ratio. Both firm value and optimal leverage ratio are decreasing functions of shareholder bargaining power.     

Utility Theory and reciprocal pairwise comparisons: The Eigenvector Method

The criticisms of Utility Theory focus on either its axioms or the construction of utility functions. Here we present a method which avoids the problems of uniqueness encountered in the construction of utility functions when using either the certainty equivalence method or the probability equivalence method. The method is based on the construction of ratio scale value functions from reciprocal pairwise comparisons and Saaty's Eigenvector Method. We show that under the assumption of cardinal consistency utility functions are a particular case of these ratio scales. Reciprocal pairwise comparisons allow decision makers to relax the transitivity assumption and help to derive a unique scaling of preferences.     

Optimal monetary policy in a new Keynesian model with animal spirits and financial markets

This article presents a macro-finance-interaction model that integrates a NKM with bounded rationality and an agent-based financial market model. We derive four interactive channels between the two sectors where two channels are strictly microfounded. We analyze the impact of the different channels on economic stability and derive optimal (conventional and unconventional) monetary policy rules. We find that coefficients of optimal Taylor rules do not significantly change if financial market stabilization becomes part of the central bank׳s objective function. Additionally, we show that rule-based, backward-looking monetary policy creates huge instabilities if expectations are boundedly rational. Our model is externally validated by showing that it generates fat tailed output growth rates.     

Statistical inference for moving‐average Lévy‐driven processes: Fourier‐based approach

We consider a new method of semiparametric statistical estimation for the continuous‐time moving‐average Lévy processes. We derive the convergence rates of the proposed estimators and show that these rates are optimal in minimax sense.     

Optimal auctions under collusion of buyers with discrete valuations

The potential seller of an indivisible good faces two potential buyers whose valuations for the good are private information. We derive the optimal selling mechanism under the assumption that the buyers collude both when the valuations are independently distributed and when they are correlated. We find that when the valuations are independent the seller can obtain the same expected revenue as if the buyers behaved noncooperatively; if instend the valuations are correlated then collusion harms the seller. In this latter case, moreover, each buyer’s information at the collusion stage about the other buyer’s valuation turns out to be very relevant for the effectiveness of collusion.     

Job matching, social network and word-of-mouth communication

Workers can find a job either directly or through personal contacts. From this micro scenario, we derive an aggregate matching function that has the standard properties but fails to be homogeneous of degree one. We show that, when the network size increases, on average, the unemployed workers hear about more vacancies through their social network. However, above a certain critical value, job matches decrease with network size. We then establish existence and uniqueness of the labor market equilibrium and study its properties. Finally, we demonstrate that the decentralized market equilibrium is not efficient because of both search and network externalities.