Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

An index formula for production economies with externalities

We prove that the degree of the equilibrium correspondence of an economy with increasing returns and external effects is equal to (−1)^L−1${(-1)}^{L-1}$ where L is the dimension of the space of goods. This allows us to infer existence, finiteness and uniqueness results.     

Satiation and existence of competitive equilibrium

In this paper, we introduce a new assumption concerning the (non)satiation property of preferences and establish the existence of a competitive equilibrium under it. The assumption is weaker than the standard nonsatiation assumption and “weak nonsatiation” introduced by Allouch and Le Van (2008). In particular, it allows preferences to be satiated only inside the set of individually rational feasible consumptions, while the two nonsatiation assumptions do not. It is also worth noting that just like the two nonsatiation assumptions, our new assumption depends solely on the characteristics of consumers.     

On the uniqueness of local equilibria

The purpose of this paper is to define a new notion of local equilibrium in an exchange economy, where the consumers face lower bounds on net trades. Then, we show that the local equilibrium is unique if the lower bounds are closed enough to 0. By the way, we also provide a convergence result of local equilibrium price toward Walras equilibrium price of a suitable tangent linear economy.     

No unbounded arbitrage,weak no market arbitrage and no arbitrage price system conditions; Equivalent conditions

Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162] prove that the no unbounded arbitrage (NUBA), a special case of a condition in Page [Page, F.H., 1987. On equilibrium in Hart’s securities exchange model. Journal of Economic Theory 41, 392–404], is equivalent to the existence of a no arbitrage price system (NAPS) when no agent has non-null useless vectors. Allouch et al. [Allouch, N., Le Van, C., Page F.H., 2002. The geometry of arbitrage and the existence of competitive equilibrium. Journal of Mathematical Economics 38, 373–391] extend the NAPS introduced by Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1403–1418] and show that this condition is equivalent to the weak no market arbitrage (WNMA) of Hart [Hart, O., 1974. On the existence of an equilibrium in a securities model. Journal of Economic Theory 9, 293–311]. They mention that this result implies the one given by Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162]. In this note, we show that all these conditions are equivalent.     

Slack in incomplete markets with nominal assets: A symmetric proof

In this paper, we provide an equilibrium analysis in the framework of incomplete markets where some agents’ preferences are possibly satiated at some state of the nature. We will consider nominal assets with exogenously fixed asset prices. We extend the notion of equilibrium with slack – introduced by Drèze and Müller [Drèze, J., Müller, H., 1980. Optimality properties of rationing schemes. Journal of Economic Theory 23, 150–159] in a fixed price setting – to the GEI framework.     

Stationary Markov equilibria on a non-compact self-justified set

The existence of stationary processes of temporary equilibria is examined in an OLG model, where there are finitely many commodities and consumers in each period, and endowments profiles and expectations profiles are subject to stochastic shocks. A state space is taken as the set of all payoff-relevant variables, and dynamics of the economy is captured as a stochastic process in the state space. In our model, however, the state space does not necessarily admit a compact-truncation consistent with the intertemporal restrictions because distributions over expectations profiles may have non-compact supports. As shown in Duffie et al. [Duffie, D., Geanakoplos, J., Mas-Colell, A., McLennan, A., 1994. Stationary Markov equilibria. Econometrica 62, 745–781), such a compact-truncation, called a self-justified set, is essential for the existence of stationary Markov equilibria. We extend their existence theorem so as to be applicable to our model.     

Direct perturbations of aggregate excess demand

We complement the Sonnenschein–Mantel–Debreu results by establishing that an exchange economy, i.e., preferences and endowments, that generates a given aggregate excess demand (AED) function is close to the economy that generates a perturbation of this AED. As a consequence, genericity and determinacy results obtained by direct perturbation of an AED are as strong as results obtained by perturbing preferences and endowments.     

The Jevons double coincidence condition and local uniqueness of money: An example

Jevons’s double coincidence of wants condition is derived as the result of household level transaction costs in general equilibrium where N   commodities are traded at (1/2)N(N−1)$(1/2)N(N-1)$ commodity-pairwise trading posts. Each household experiences a set-up cost on entering an additional trading post. Budget constraints are enforced at each trading post separately implying demand for a carrier of value between trading posts, commodity money. General equilibrium consists of prices so that each trading post clears. Existence and local uniqueness of commodity money in equilibrium can follow from the scale economy implied by the household set-up cost.     

Nonparametric tests of collectively rational consumption behavior: An integer programming procedure

We present an IP-based nonparametric (revealed preference) testing procedure for rational consumption behavior in terms of a general collective model, which includes consumption externalities and public consumption. An empirical application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the practical usefulness of the procedure. Finally, we present extensions of the testing procedure to evaluate the goodness-of-fit (accounting for optimization error as well as measurement error) of the collective model subject to testing.     

Estimating high-dimensional demand systems in the presence of many binding non-negativity constraints

Two econometric issues arise in the structural estimation of consumer or producer demand systems in the presence of many binding non-negativity constraints. Firstly, most existing methods entail the evaluation of multivariate probability integrals. Secondly, the issue of statistical coherency must be addressed. We circumvent both of these issues using Gibbs’ Sampling, along with data augmentation and rejection sampling. We illustrate our method using several simulated data sets.     

Equilibrium in a mixed economy of arrow-debreu type

The functioning of the current NIS economies is severely affected by regulatory interferencies with supply and demand for many commodities. In particular, the presence of dual markets is characteristic for these economies. On the first market, typically the “low-price sector” of the economy, prices are fixed and the allocation of goods is determined by rationing schemes and governmental orders. On the second market, flexible prices resulting from the market mechanism coordinate demand and supply. It is allowed that any surplus of good purchased on the first market can be sold on the second market at the then prevailing market prices.     

Strictly monotonic preferences on continuum of goods commodity spaces

We consider a set K of differentiated commodities. A preference relation on the set of consumption plans is strictly monotonic whenever to consume more of at least one commodity is more preferred. It is an easy task to find examples of strictly monotonic preference relations when K   is finite or countable. However, it is not easy for spaces like ?^∞([0,1])${?}^{\infty }([0\text{,}1])$, the space of bounded functions on the unit interval.     

Regression density estimation using smooth adaptive Gaussian mixtures

We model a regression density flexibly so that at each value of the covariates the density is a mixture of normals with the means, variances and mixture probabilities of the components changing smoothly as a function of the covariates. The model extends the existing models in two important ways. First, the components are allowed to be heteroscedastic regressions as the standard model with homoscedastic regressions can give a poor fit to heteroscedastic data, especially when the number of covariates is large. Furthermore, we typically need fewer components, which makes it easier to interpret the model and speeds up the computation. The second main extension is to introduce a novel variable selection prior into all the components of the model. The variable selection prior acts as a self-adjusting mechanism that prevents overfitting and makes it feasible to fit flexible high-dimensional surfaces. We use Bayesian inference and Markov Chain Monte Carlo methods to estimate the model. Simulated and real examples are used to show that the full generality of our model is required to fit a large class of densities, but also that special cases of the general model are interesting models for economic data.     

Club theory and household formation

The relationship between our general equilibrium model with multi-member households and club models with multiple private goods is investigated. The main distinction in the definitions consists in the equilibrium concepts. As a rule, competitive equilibria among households where no group of consumers can benefit from forming a new household and valuation equilibria prove equivalent in the absence of consumption externalities, but not in their presence.     

Agglomeration economies with consistent productivity estimates

This paper investigates the relative impact of microeconomic agglomeration mechanisms on plant's total factor productivity (TFP) using German establishment and employment-level data. Contrasting different strategies for estimating TFP from plant-level production functions reveals that unobserved output prices bias true productivity and lead to underestimated agglomeration economies. With the corrected TFP measure, the largest impact is found for labor market pooling, which is captured by the correlation of the occupational composition between one county-industry and the rest of the county. This main result is robust, even when the spatial units are resized from counties to larger labor market regions. Input linkages appear to be relevant only at this larger regional scale. Overall, agglomeration economies differ substantially across industries. Only for a subset of industries, some positive evidence is detected for knowledge spillovers.     

Nonparametric and semiparametric regressions subject to monotonicity constraints: Estimation and forecasting

This paper considers nonparametric and semiparametric regression models subject to monotonicity constraint. We use bagging as an alternative approach to Hall and Huang (2001). Asymptotic properties of our proposed estimators and forecasts are established. Monte Carlo simulation is conducted to show their finite sample performance. An application to predicting equity premium is taken for illustration. We introduce a new forecasting evaluation criterion based on the second order stochastic dominance in the size of forecast errors and compare models over different sizes of forecast errors. Imposing monotonicity constraint can mitigate the chance of making large size forecast errors.     

Time reversibility of stationary regular finite-state Markov chains

We propose an alternate parameterization of stationary regular finite-state Markov chains, and a decomposition of the parameter into time reversible and time irreversible parts. We demonstrate some useful properties of the decomposition, and propose an index for a certain type of time irreversibility, applicable to chains whose states are naturally ordered. Two empirical examples illustrate the use of the proposed parameter, decomposition and index. One, on gasoline price mark-ups, involves observed states. The other, on U.S. investment growth, features latent states.     

Extreme points of two digraph polytopes: Description and applications in economics and game theory

In this paper, we introduce two polytopes that respect a digraph in the sense that for every vector in the polytope every component corresponds to a node and is at least equal to the component corresponding to each successor of this node. The sharing polytope is the set of all elements from the unit simplex that respect the digraph. The fuzzy polytope is the set of all elements of the unit cube respecting the digraph. The main results are characterizations of the extreme points of the above described two digraph polytopes. We also give an economic application of the result on the sharing polytope and a game-theoretical application for the fuzzy polytope.