Optimal control problems from second-order difference equations

We examine solutions x?l_∞(Rⁿ) of the equations $\text{F}{}_{\mathrm{t}}\text{(}\text{x}{}_{\mathrm{t?1}}\text{,}\text{x}{}_{\mathrm{t}}\text{,}\text{x}{}_{\mathrm{t+1}}\text{) = 0}$ and derive conditions for the existence of objective functions G_t so that $\text{x}$ solves max_x?l∞ΣG_t(x_t, x_t+1). We specialize the conditions to time autonomous equations and apply them to a competitive industry in temporary equilibrium. The objective function in the example is of the cost-benefit form: consumer surplus minus opportunity cost of labor minus industry-wide cost of investment.     

A new test for normality

Burr (1942) type XII distribution $\text{?(u)=kc u}{}^{\mathrm{c?1}}\text{(1+u}{}^{\mathrm{c}}\text{)}{}^{\mathrm{-(k+1)}}\text{u?0, k > 0, c > 0}$ is considered. Particular values of k and c give β₁ ? 0 and β₂ ? 3. Using this fact tests for normality of observations and regression disturbances are constructed.u.1. Introduction     

Sufficient conditions in free final time optimal control problems. A comment

By an application of sufficient conditions, assume that an optimal pair (χ_τ(·), u_τ(·)) and an adjoint function p_τ(·) were found in the control problem in question with the final time τ fixed but arbitrary. Then a sufficient condition for one of these pairs, say , to be optimal in the corresponding free final time problem is that the Hamiltonian, with (χ_τ(t), u_τ(τ?), p_τ(τ), τ) inserted, is nonnegative (nonpositive) to the left (right) of $\text{τ}{}^1$.     

Transfer principles in income redistribution

Dalton's principle of transfer for income redistribution says that society will be better off when a unit of income in transferred from a richer to a poorer individual. This paper investigates the conjunction of a natural extension of Dalton's principle — which says that any combination of a socially desirable transfer with its inverse at uniformly higher levels of income will have positive social benefit — and a traditional utilitarian-egalitarian formulation of social welfare. The transfer principles involved in the extension of Dalton's rule correspond to stochastic dominance relations between income distributions with a common mean, and lead to the conclusion that, when ? and g are income distributions, the social welfare of ? is larger than that of g if $\text{Σe}{}^{\mathrm{-ax}}\text{?(x)<Σe}{}^{\mathrm{-ax}}\text{g(x)}$ for all positive a. This conclusion is intimately connected with a measure of income inequality studied by Kolm.     

Disequilibrium theory,waiting costs,and saving behavior in centrally planned economies: A queueing-theoretic approach

An expected-utility maximizer, obliged to make a single purchase from two alternatives, finds that a queue forms for the good that would have been selected had both goods been available. An M/M/1 queue is posited and for each period of delay the maximum additional payment $\text{b}{}^1$ that the consumer would incur to join the queue is determined. This has implications for saving. Not only the availability of the good, but also the delay in obtaining it, the alteration in its arrival rate, and the “stampede effect” determine saving behavior.     

A note on the generalised measures of risk aversion

This paper is concerned with generalised scalar measures of risk aversion. A measure R which may meaningfully be applied to both unidimensional risks (risk in income or wealth) and multidimensional risks has been constructed. In case of identical preferences, we have also constructed an alternative measure of risk aversion $\text{R}{}^1$ which is shown to be related to the Khilstrom-Mirman measure. This relationship explains the nature of the Khilstrom-Mirman measure.     

Core allocations and the dimension of the cone of efficiency price vectors

Let (R₁,…,R_k) be an arbitrary partition of the grand coalition in an atomless exchange economy with k “large enough.” We prove that an optimal allocation x belongs to the core if and only if x cannot be improved upon by any coalition that includes at least one of the R_i's. K is “large enough” if k ? r + 1, where r is the linear dimension of the cone P of the efficiency price vectors for x. Recall that it is always true that r ? n, when n is the number of commodities in the market, and that under differentiability and interiority r = 1; thus k can be chosen to be 2 (i.e., for any coalition R, an allocation x belongs to the core of the market if and only if x is not blocked by any coalition that either contains R or contains its complement).     

When is a tax neutral?

A proportional income tax is said to be neutral if variations in the tax rate do not affect the optimal composition of the consumption commodities of a utility maximizing consumer. It is shown that neutrality obtains if and only if the indirect utility function of the consumer is groupwise homothetic. If the income tax rates on labor and property incomes are allowed to differ, then neutrality obtains if and only if the indirect utility function of the consumer is homothetically separable. If, in addition, it is required that the proportional income tax be neutral with respect to not only consumption commodities but also to leisure, then 'the indirect utility function must have the form: $\text{V = V(f(w)+H}{}^1\text{(p))}$, where w and p are the normalized prices of leisure and consumption respectively, and H¹(p) is homogeneous of degree one in p.     

Partial identification in binary response models with nonignorable nonresponses

This study investigates the identification of parameters in semiparametric binary response models of the form y=1(x^′β+v+ε>0)$y=1(x^{\prime }\beta +v+\epsilon >0)$ when there are nonignorable nonresponses. We propose an estimation procedure for the identified set, the set of parameters that are observationally indistinguishable from the true value β$\beta$, based on the special regressor approach of Lewbel (2000). We show that the estimator for the identified set is consistent in the Hausdorff metric.     

Extreme value statistics and recurrence intervals of NYMEX energy futures volatility

Energy markets and the associated energy futures markets play a crucial role in global economies. It is of great theoretical and practical significance to gain a deeper understanding of extreme value statistics of the volatility of energy futures traded on the New York Mercantile Exchange (NYMEX). We investigate the statistical properties of the recurrence intervals of daily volatility time series of four NYMEX energy futures, which are defined as the waiting times τ between consecutive volatilities exceeding a given threshold q. We find that the recurrence intervals are distributed as a stretched exponential $P_q\left(\tau \right)\sim e^{{\left(\mathit{a\tau }\right)}^{-\gamma }}$, where the exponent γ decreases with increasing q, and there is no scaling behavior in the distributions for different thresholds q after the recurrence intervals are scaled with the mean recurrence interval $\overline{\tau }$. These findings are significant under the Kolmogorov–Smirnov test and the Cramér–von Mises test. We show that the empirical estimations are in nice agreement with the numerical integration results for the occurrence probability W_q(Δt|t) of a next event above the threshold q within a (short) time interval after an elapsed time t from the last event above q. We also investigate the memory effects of the recurrence intervals. It is found that the conditional distributions of large and small recurrence intervals differ from each other and the conditional mean of the recurrence intervals scale as a power law of the preceding interval $\overline{\tau }\left({\tau }_0\right)/\overline{\tau }\sim {\left({\tau }_0/\overline{\tau }\right)}^{\beta }$, indicating that the recurrence intervals have short-term correlations. Detrended fluctuation analysis and detrending moving average analysis further uncover that the recurrence intervals possess long-term correlations. We confirm that the “clustering” of the volatility recurrence intervals is caused by the long-term correlations well known to be present in the volatility. Our findings shed new lights on the behavior of large volatilities and have potential implications in risk management of energy futures.     

A Hausman–Taylor instrumental variable approach to the penalized estimation of quantile panel models

This paper proposes an _?1${?}_1$ penalized quantile regression estimator which adapts the Hausman–Taylor instrumental variable approach in order to address the bias resulting from the shrinkage of the individual effects.     

The Debreu private ownership economy with complementary commodities and prices

Let E_p be a Debreu private ownership economy in which there are some complementary commodities. It means that all commodity bundles are contained in the proper subspace V   of commodity–space [R]l(l∈{1,2,…})${\mathfrak{[R]}}^l\left(l\in \left\{1,2,\dots \right\}\right)$. The production plans maximizing the producers' profits do not have to satisfy the dependency in the qualities of commodities seen in the consumers' plans. It may cause no-existence an equilibrium in economy E_p. The competitive leads, however, to adjustment the production plans to improve the consumers' satisfaction. The procedure of change the production system covering the consumers' requirements is presented. As a result, the model of the private ownership economy with complementary commodities and prices, being the simplification of the initial model, is elaborated. Consequently, the necessary condition for the existence of an equilibrium in the economy E_p is proved.     

The functional central limit theorem for ARMA–GARCH processes

In this paper, we study the functional central limit theorem for ARMA–GARCH processes. We prove that, under the finite second moment assumption, the stationary ARMA–GARCH process is geometrically_L2$L_2$-NED and that the functional central limit theorem holds.