Stationarity and the existence of moments of a family of GARCH processes

This paper investigates some structural properties of a family of GARCH processes. A simple sufficient condition for the existence of the αδ-order stationary solution of the processes is derived, where α∈(0,1] and δ>0. The solution is strictly stationary and ergodic, and the causal expansion of the family of GARCH processes is also established. Furthermore, the necessary and sufficient condition for the existence of the moments is obtained. The technique used in this paper for the moment conditions is different from that used in He and Terasvirta (J. Econom. 92 (1999a) 173), and avoids the assumption that the process started at some finite value infinitely many periods ago. Moreover, the conditions for the strict stationarity of the model and the existence of its moments are simple to check and should prove useful in practice.     

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.     

Some large-concentration-parameter asymptotics for the k-class estimators

A sufficient condition is derived in this paper for the consistency and asymptotic normality of the k-class estimators (k-stochastic or nonstochastic) as the concentration parameter increases indefinitely, with the sample size either staying fixed or also increasing. It is further shown that the limited-information maximum likelihood estimator satisfies this condition. Since large sample size implies a large concentration parameter, but not vice versa, the usual conditions for consistency and asymptotic normality of the k-class estimators as the sample size increases can be inferred from the results given in this paper. But more importantly, the results in this paper shed further light on the small-sample properties of the stochastic k-class estimators and can serve as a starting point for the derivation of asymptotic approximations for these estimators as the concentration parameter goes to infinity, while the sample size either stays fixed or also goes to infinity.     

On top responsiveness and strict core stability

Alcalde and Revilla [Journal of Mathematical Economics 40 (2004) 869–887] introduce a top responsiveness condition on players’ preferences in hedonic games and show that it guarantees the existence of a core stable partition. In the present note we strengthen this observation by proving that under top responsiveness even the strict core is non-empty.     

The graph of the k-class estimator: An algebraic and statistical interpretation

This paper presents an algebraic analysis of the graphs of the k-class estimator, its asymptotic standard error and asymptotic t-ratio as functions of k for a single structural equation containing one or more endogenous explanatory variables. These results are illustrated by the corresponding graphs of the second and fifth equations of the Girshick-Haavelmo (1947) Demand for Food Model.Tests of the rank condition for identification are also developed. They are found to involve the values of k which explode the k-class estimator.     

Several efficient two-step estimators for the dynamic simultaneous equations model with autoregressive disturbances

Several asymptotically efficient methods are suggested on both the full and the limited information approach to estimate the simultaneous equations model in which the lagged endogenous variables and the autoregressive disturbances coexist. They are two-step procedures and do not involve iterations. A method is suggested also for the case where any portion of the autoregressive parameter matrix is specified to be zero. Since the consistency and efficiency depend upon the asymptotic, local identifiability, the necessary and sufficient condition is derived for it. It does not depend on the exclusion of the lagged endogenous variables.     

Separating Information Maximum Likelihood estimation of the integrated volatility and covariance with micro-market noise

For estimating the integrated volatility and covariance by using high frequency financial data, we propose the Separating Information Maximum Likelihood (SIML) method when there are possibly micro-market noises. The resulting estimator, which is represented as a specific quadratic form of returns, is simple and their properties have been investigated by [Kunitomo and Sato, 2008a], [Kunitomo and Sato, 2008b], [Kunitomo and Sato, 2010], [Kunitomo and Sato, 2011]. We show that the SIML estimator has reasonable asymptotic properties; it is consistent and it has the asymptotic normality when the sample size is large and the integrated volatility is deterministic under general conditions including some non-Gaussian and volatility models. Based on simulations, we find that the SIML estimator has reasonable finite sample properties and it would be useful for practice. The SIML estimator has the asymptotic robustness properties in the sense it is consistent when the noise terms are weakly dependent and they are endogenously correlated with the efficient market price process. We illustrate the use of SIML by analyzing Nikkei-225 futures, which are the derivatives of the major stock index in Japan.     

The zero-information-limit condition and spurious inference in weakly identified models

In many econometric models the asymptotic variance of a parameter estimate depends on the value of another structural parameter in such a way that the data contain little information about the former when the latter is close to a critical value. This paper introduces the zero-information-limit-condition (ZILC) to identify such models where ‘weak identification’ leads to spurious inference. We find that standard errors tend to be underestimated in these cases, but the size of the asymptotic t-test may either be too great (the intuitive case emphasized in the ‘weak instrument’ literature) or too small as in two cases illustrated here.     

Testing the autoregressive parameter with the t statistic

This paper considers a Gaussian first-order autoregressive process with unknown intercept where the initial value of the variable is a known constant. Monte Carlo simulations are used to investigate the sampling distribution of the t statistic for the autoregressive parameter when its value is in the neighborhood of unity. A small sigma asymptotic result is exploited in the construction of exact non-similar tests. The powers of non-similar tests of the random walk and other hypotheses are estimated for sample sizes typical in economic applications.     

Non-Walrasian decentralization of the core

We show that in large finite economies, core allocations can be approximately decentralized as Nash (rather than Walras) equilibrium. We argue that this exercise is an essential complement to asymptotic core equivalence results, because it implies that in some approximate sense individual attempts to manipulate the decentralizing prices cannot be beneficial, which fits precisely the interpretation of asymptotic core convergence, namely the emergence of price taking.     

Berry-Esséen rate in asymptotic normality for perturbed sample quantiles

In estimating quantiles with a sample of sizeN obtained from a distributionF, the perturbed sample quantiles based on a kernel functionk have been investigated by many authors. It is well known that their behaviour depends on the choices of “window-width”, sayw _N. Under suitable and reasonably mild assumptions onF andk, Ralescu and Sun (1993) have recently proven that lim _N→∞ N ^1/4w_N=0 is the necessary and sufficient condition for the asymptotic normality of the perturbed sample quantiles. In this paper, their rate of convergence is investigated. It turns out that the optimal Berry-Esséen rate ofO(N^?1/2) can be achieved by choosing the window-width suitably, sayw _N=O(N^?1/2). The obtained results, in addition to being explicit enough to verify the sufficient condition for the asymptotic normality, improve Ralescu's (1992) result of which the rate is of order (logN)N ^?1/2.     

Content horizons for univariate time-series forecasts

This paper investigates the maximum horizon at which conditioning information can be shown to have value for univariate time series forecasts. In particular, we consider the problem of determining the horizon beyond which forecasts from univariate time series models of stationary processes add nothing to the forecast implicit in the unconditional mean. We refer to this as the content horizon for forecasts, and provide a formal definition of the corresponding forecast content function at horizons s=1,… S. This function depends upon parameter estimation uncertainty as well as on autocorrelation structure of the process. We show that for autoregressive processes it is possible to give an asymptotic expression for the forecast content function, and show by simulation that the expression gives a good approximation even at modest sample sizes. The results are applied to the growth rate of GDP and to inflation, using US and Canadian data.     

Testing for stochastic dominance using the weighted McFadden-type statistic

We demonstrate that when testing for stochastic dominance of order three and above, using a weighted version of the Kolmogorov–Smirnov-type statistic proposed by McFadden [1989. In: Fomby, T.B., Seo, T.K. (Eds.), Studies in the Economics of Uncertainty. Springer, New York, pp. 113–134] is necessary for obtaining a non-degenerate asymptotic distribution. Since the asymptotic distribution is complex, we discuss a bootstrap approximation for it in the context of a real application.     

Envy-freeness and implementation in large economies

We show that an asymptotic envy-freeness condition is necessary for a form of robust approximate implementation in large economies. In settings where allocations are excludable, asymptotic envy-freeness is also sufficient for implementation, while in non-excludable settings it is not sufficient.     

Improving impact of research papers

This editorial aims to assist authors in maximizing the impact of their work. While the editorial is written specifically for the journal Technovation, many items of advice are equally applicable to other publishing outlets. While the value of any article is its unique core contribution, the best way to present an article's core value is quite consistent and is the focus of this editorial.     

The geometry of arbitrage and the existence of competitive equilibrium

We present the basic geometry of arbitrage, and use this basic geometry to shed new light on the relationships between various no-arbitrage conditions found in the literature. For example, under very mild conditions, we show that the no-arbitrage conditions of Hart [Journal of Economic Theory 9 (1974) 293] and Werner [Econometrica 55 (1987) 1403] are equivalent and imply the compactness of the set of utility possibilities. Moreover, we show that if agents’ sets of useless net trades are linearly independent, then the Hart–Werner conditions are equivalent to the stronger condition of no-unbounded-arbitrage due to Page [Journal of Economic theory 41 (1987) 392]—and, in turn, all are equivalent to compactness of the set of rational allocations. We also consider the problem of existence of equilibrium. We show, for example, that under a uniformity condition on preferences weaker than Werner’s uniformity condition, the Hart–Werner no-arbitrage conditions are sufficient for existence. With an additional condition of weak no-half-lines—a condition weaker than Werner’s no-half-lines condition—we show that the Hart–Werner conditions are both necessary and sufficient for existence.     

人本视角中的社会主义核心价值体系

从马克思主义人本视角出发,社会主义核心价值体系是以人的需要为基础、以人的社会性存在为基本内容,以人的创价值活动为旨向,使其具有丰富的人本意蕴。     

Asymptotic stability of a general equilibrium under perfect and monopolistic competition

This study examines the asymptotic stability of a general equilibrium for an economy under perfect and monopolistic competition in which delays in a production process arise. Crucially, we find that the sufficient conditions for the stability of the equilibrium in each model differ markedly. For the stability of the equilibrium under perfect (monopolistic) competition, it is favorable that the slope of every demand curve is gradual (steep).     

Coalition production economies with divisible and indivisible inputs: Asymptotic results

This paper investigates the asymptotic characteristics of the relations between the Shapley value and the core of replicated production economies with divisible and indivisible inputs.