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The many-agent Ramsey model (MARM) without integrated capital markets (ICM) gives income convergence. Analysis indicates that the problem with the original Ramey model may not be that it is special case of Koopmans recursive preferences, but rather it is an instance of Koopmans recursive preferences.

A small deviation in one variable can engender significant convergence rate variation in a one-sector production growth model.

Maximum likelihood estimation in finite mixture distributions is typically approached as an incomplete data problem to allow application of the expectation-maximization (EM) algorithm. In its general formulation, the EM algorithm [...]

Human capital and per capita income growth were parallel in Canada during 1951-1996, validating the growth model of Barro et al. The model indicates that higher education levels are good predictors of long term economic growth. State resources could be distributed to outlying areas to achieve growth throughout the country.

This paper extends the theoretical analysis of the spurious regression and spurious detrending from the usual I(1) processes to the long memory fractionally integrated processes. It is found that when we regress a long memory fractionally integrated process on another unrelated long memory fractionally integrated process, no matter whether these processes are stationary or not, as long as their orders of integration sum up to a value greater than 0.5, the t ratios become divergent and spurious effects occur. Our finding suggests that it is the long memory, instead of nonstationarity or lack of ergodicity, that causes such spurious effects. As a result, spurious effects might happen more often than we previously believed as they can arise even between stationary series while the usual first-differencing procedure may not completely eliminate spurious effects when data possess strong long memory.

The hypothesis of cross-country convergence of levels and growth rates of income per capita implied by the neo-classical growth model in the Solow-Swan as well as in the Rampsey-Cass-Koopmans versions is investigated. Convergence to a common income level as opposed to divergence is seen from a theoretical perspective. The convergence property is then empirically tested. Results cast doubt on Barro type regressions and their findings about 'conditional' convergence.

This paper presents a model of a discrete-time recurrent neural network designed to perform quadratic real optimization with bound constraints. The network iteratively improves the estimate of the solution, always maintaining it inside of the feasible region. Several neuron updating rules which assure global convergence of the net to the desired minimum have been obtained. Some of them also assure exponential convergence and maximize a lower bound for the convergence degree. Simulation results are presented to show the net performance. Index Terms - Convergence of numerical methods, discrete-time systems, gradient methods, optimization methods, recurrent neural networks.

This paper gives general conditions for convergence rates and asymptotic normality of series estimators of conditional expectations, and specializes these conditions to polynomial regression and regression splines. Both mean-square and uniform convergence rates are derived. Asymptotic normality is shown for nonlinear functionals of series estimators, covering many cases not previously treated. Also, a simple condition for [square root of n]-consistency of a functional of a series estimator is given. The regularity conditions are straightforward to understand, and several examples are given to illustrate their application. Key words: Nonparametric estimation; Series estimation; Convergence rates; Asymptotic normality

Equivalence core and the set of Walrasian allocations have been used as a basic test of perfect economic competition. A study of these tests used core convergence theorem models, such as those of Debreu-Scarf (1963), and Aumann's (1964) to establish the competitiveness of core allocations in economies with infinite dimensional space of commodities and large number of finite agents. Analyses showed that treating the various types of labor as elements of an infinite dimensional commodity space can demonstrate labor endowments of specific individuals are close substitutes.

Constant price GDP measures are not true quantity indexes because they are prone to substitution bias and they distort income level measurements of convergence and divergence. The Ideal Afriat Index is proposed as a new multilateral index that establishes limits to the variance of true quantity indexes. Findings reveal that constant price indexes of GDP are inclined to misinterpret the measurement of convergence in true GDP with convergence in prices.

Two theories can account for the development and implementation of pension benefits for different countries. The convergence theory explains outcome similarities, or the tendency for comparative population groups to obtain comparative benefits. The politics matter theory explains the dissimilarities in the organizational structures that dispense these benefits, even though outcomes are similar., Scandinavia and Australia share a similar sequence of pension-political developments. Starting out from means-tested minimum pensions, these countries have moved towards a dual mandatory pension structure in which the working [...]

Stochastic analysis of Rosenblatt's single layer perceptron algorithm for fast learning shows convergence features. Convergence points of the algorithm depend on variance of input signal, and the step size mu, with the algorithm being stable for all mu > 0. The convergence is also studied to find out the effects of noisy perceptron input vectors.

Gersgorin's theorem or Taussky's theorem is used to find a new unified proof for the convergence of Jacobi and Gauss-Seidel iterative methods. Many systems of linear equations are solved using these two methods. The basis of solving linear equations is either strict diagonal dominance of matrix or diagonal dominance and irreducibility of matrix. The theorem to be used depends on the criterion used. The mathematical steps involved in both criteria are similar and could make an interesting teaching topic.

MAXNET is a common competitive architecture to select the maximum or minimum from a set of data. However, there are two major problems with the MAXNET. The first problem is its slow convergence rate if all the data have nearly the same value. The second one is that it fails when either nonunique extreme values exist or each initial value is smaller than or equal to the sum of initial inhibitions from other nodes. In this paper, a novel neural network model called SELECTRON is proposed to select the maxima or minima from a set of data. This model is able to select all the maxima or minima via competition among the processing units even when MAXNET fails. We will then prove that SELECTRON converges to the correct state in every situation. In addition, the convergence rates of SELECTRON for three special data distributions will be derived. Finally, simulation results indicate that SELECTRON converges much faster than MAXNET.

Adaptive learning algorithms using nonlinear dynamic processes have been developed to analyze the behavior of economic agents. The algorithms can prove useful in analyzing moderate dependence behavior such as mixing and mixingale processes. However, the algorithms fail to give correct belief equilibria even when used with correctly specified nonlinear models. A discussion of the implications of the results on future directions of research are presented.

The traditional approach to the mathematical theory of dynamic programming incorporates an abstract contraction property known as Lipschitz condition. Biconvergence is a suggested alternative approach that embodies an abstract topological condition on both the utility function and the intertemporal production correspondence. Biconvergence is easier to test, and results are less difficult to interpret.

The relevant rule of thumb and the polynomials of high degree providing one stays well away from the boundary of the disc of convergence is detailed.

This paper is concerned with the on-line learning of unknown dynamical systems using a recurrent neural network. The unknown dynamic systems to be learned are subject to disturbances and possibly unstable. The neural-network model used has a simple architecture with one layer of adaptive connection weights. Four learning rules are proposed for the cases where the system state is measurable in continuous or discrete time. Some of these learning rules extend the [Sigma]-modification of the standard gradient learning rule. Convergence properties are given to show for the recurrent neural network is demonstrated using an illustrative example of tracking a Brownian motion. Index Terms--Dynamic systems, model mismatch, on-line learning.

The use of adaptive linear techniques to solve signal processing problems is needed particularly when the interference environment external to the signal processor (such as for a radar or communication system) is not known a priori. Due to this lack of knowledge of an external environment, adaptive techniques require a certain amount of data to cancel the external interference. The number of statistically independent samples per input sensor required so that the performance of the adaptive processor is close (nominally within 3 dB) to the optimum is called the convergence measure of effectiveness (MOE) of the processor. The minimization of the convergence MOE is important since in many environments the external interference changes rapidly with time. Although there are heuristic techniques in the literature such as the Eigenvector Projection Method (EPM) that provide fast convergence for particular problems, there is currently not a general solution for arbitrary interference that is derived via classical theory. A maximum likelihood (ML) solution (under the assumption that the input interference is Gaussian) is derived here for a structured covariance matrix that has the form of the identity matrix plus an unknown positive semi-definite Hermitian (PSDH) matrix. This covariance matrix form is often valid in realistic interference scenarios for radar and communication systems. Using this ML estimate, simulation results are given that show that the convergence is much faster than the often-used sample matrix inversion (SMI) method. In addition, the ML solution for a structured covariance matrix that has the aforementioned form where the scale factor on the identity matrix is arbitrarily lower-bounded, is derived. Finally, an efficient implementation is presented.

The convergence properties of an extended source separation neural network proposed by Cichocki et al based on the classical Herault-Jutten network are analyzed. The equilibrium points as well as the stability of the network fr a small adaptation gain are considered. It is shown that the stationary independent sources that can be separated by the neural network are the globally sub-Gaussian signals. A modified version of the network is derived that proves the theoretical results through computer simulations.