Approximations of the eigenvalues of the covariance matrix of a first-order autoregressive process

This paper provides explicit estimates of the eigenvalues of the covariance matrix of an autoregressive process of order one. Also explicit error bounds are established in closed form. Typically, such an error bound is given by $\text{ε}{}_{\mathrm{k}}\text{= (}\text{4}\text{(n+1)}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{ρ}{}^2\text{sin}\text{(}\text{kπ}\text{(n+1)}\text{)}$, so that the approximations improve as the size of the matrix increases. In other words, the accuracy of the approximations increases as direct computations become more costly.     

Botswana's Macroeconomic Management of Its Mineral-Based Growth: It Used Mining Revenues for Development and Services but Must Now Broaden the Beneficiaries

Abstract . The economic performance and the political history of Botswana during 1974-84 contrasted significantly with the experience of virtually every other African country. The South African republic, immediately north of the Republic of South Africa, achieved steady real economic growth with improved social services and provision for its people's basic needs. This was achieved in spite of world recession and drought because its mineral wealth Was reserved for the people and mining companies had to pay for the privilege of extracting that wealth through a tax program limited to appropriating its surplus, while assuring the investors and entrepreneurs an adequate long-term return on capital and enterprise. But sound macroeconomic policies failed to provide even reasonably equitable benefits for the majority of the people. Sound micropolicies are needed to widen access to employment and earned income and to asset accumulation.     

Convergence of a branching type recursion with non-stationary immigration

The asymptotic distribution of a branching type recursion with non-stationary immigration is investigated. The recursion is given by , where (X _l ) is a random sequence, (L _n ⁻¹⁽¹⁾ ) are iid copies ofL _n−1,K is a random number andK, (L _n ⁻¹⁽¹⁾ ), {(X _l ),Y _n } are independent. This recursion has been studied intensively in the literature in the case thatX _l ≥0,K is nonrandom andY _n =0 ∀n. Cramer, Rüschendorf (1996b) treat the above recursion without immigration with starting conditionL ₀=1, and easy to handle cases of the recursion with stationary immigration (i.e. the distribution ofY _n does not depend on the timen). In this paper a general limit theorem will be deduced under natural conditions including square-integrability of the involved random variables. The treatment of the recursion is based on a contraction method. The conditions of the limit theorem are built upon the knowledge of the first two moments ofL _n . In case of stationary immigration a detailed analysis of the first two moments ofL _n leads one to consider 15 different cases. These cases are illustrated graphically and provide a straight forward means to check the conditions and to determine the operator whose unique fixed point is the limit distribution of the normalizedL _n .     

Two-sample rank tests with truncated populations

LetX ₁,…,X _m andY ₁,…,Y _n be two independent samples from continuous distributionsF andG respectively. Using a Hoeffding (1951) type theorem, we obtain the distributions of the vector S=(S ₍₁₎,…,S _(n)), whereS _(j)=# (X _i ’s≤Y _(j)) andY _(j) is thej-th order statistic ofY sample, under three truncation models: (a)G is a left truncation ofF orG is a right truncation ofF, (b)F is a right truncation ofH andG is a left truncation ofH, whereH is some continuous distribution function, (c)G is a two tail truncation ofF. Exploiting the relation between S and the vectorR of the ranks of the order statistics of theY-sample in the pooled sample, we can obtain exact distributions of many rank tests. We use these to compare powers of the Hajek test (Hajek 1967), the Sidak Vondracek test (1957) and the Mann-Whitney-Wilcoxon test. We derive some order relations between the values of the probagility-functions under each model. Hence find that the tests based onS ₍₁₎ andS _(n) are the UMP rank tests for the alternative (a). We also find LMP rank tests under the alternatives (b) and (c).     

Combining information for prediction in linear regression

This article deals with the prediction problem in linear regression where the measurements are obtained using k different devices or collected from k different independent sources. For the case of k=2, a Graybill-Deal type combined estimtor for the regression parameters is shown to dominate the individual least squares estimators under the covariance criterion. Two predictors ŷ _c and ŷ _p are proposed. ŷ _c is based on a combined estimator of the regression coefficient vector, and ŷ _p is obtained by combining the individual predictors from different models. Prediction mean square errors of both predictors are derived. It is shown that the predictor ŷ _p is better than the individual predictors for k≥2 and the predictor ŷ _c is better than the individual predictors for k=2. Numerical comparison between ŷ _c and ŷ _p shows that the former is superior to the latter for the case k=2.     

Henry George's Theory of State's Agenda: The Origins of His Ideas on Economic Policy in Adam Smith's Moral Theory

Abstract . The tension between Henry George's reformism and his laissezfaire liberalism was resolved through a system of natural liberty George derived from the relation between Adam Smith's ethics and economics. Crucial for George's nonutilitarian philosophy of government was the interdependence between the moral sense (sympathy) and the prevailing socioeconomic order. In the appropriate institutional environment, the role of the government was diminished since the pervasive moral sense insured justice by monitoring the individual's pursuit of economic self-interest. In contrast, a defective socio economic order required government intervention. For example, land monopoly and the maldistribution of income undermined the role of sympathy, promoted excessive self interest and the breakdown of the system of natural liberty. Government action through the single tax eliminated the “fear of want,” restored an operative moral sense and guaranteed justice in society. Under these conditions, government can provide additional services for a growing society without being susceptible to “corrupt and tyrannous” behavior.     

Information in generalized method of moments estimation and entropy-based moment selection

In this paper, we make five contributions to the literature on information and entropy in generalized method of moments (GMM) estimation. First, we introduce the concept of the long run canonical correlations (LRCCs) between the true score vector and the moment function f(_vt,_θ0)$f(v_t,{\theta }_0)$ and show that they provide a metric for the information contained in the population moment condition E[f(_vt,_θ0)]=0$\mathrm{E}[f(v_t,{\theta }_0)]=0$. Second, we show that the entropy of the limiting distribution of the GMM estimator can be written in terms of these LRCCs. Third, motivated by the above results, we introduce an information criterion based on this entropy that can be used as a basis for moment selection. Fourth, we introduce the concept of nearly redundant moment conditions and use it to explore the connection between redundancy and weak identification. Fifth, we analyse the behaviour of the aforementioned entropy-based moment selection method in two scenarios of interest; these scenarios are: (i) nonlinear dynamic models where the parameter vector is identified by all the combinations of moment conditions considered; (ii) linear static models where the parameter vector may be weakly identified for some of the combinations considered. The first of these contributions rests on a generalized information equality that is proved in the paper, and may be of interest in its own right.     

Some Determinants of Property Crime: Economic Factors Influence Criminal Behavior But Cannot Completely Explain the Syndrome

Abstract . An empirical analysis of the property crimes, robbery, burglary and larceny, is presented for all 120 counties in Kentucky. While this analysis is based on an economic model of crime, certain sociological and legal variables are included as well in the system of equations. Overall, the empirical results support prior studies’findings with the exception that a quadratic relationship is found to exist between urbanization and each of the property crimes. Furthermore, neither the economic nor the non economic influences measured appear more important for affecting crime rates. Specifically, results indicate that the level of poverty, the degree of tourism, the presence of police, the unemployment rate and the apprehension rate all affect property crimes. In contrast, the length of sentence, the degree of industrialization, the level of public assistance payments and the proportion of youth in the county have no affect on property crime rates in these areas.     

Bounds for the mean residual life function of a <Emphasis Type="Italic">k</Emphasis>-out-of-<Emphasis Type="Italic">n</Emphasis> system

In the reliability studies, k-out-of-n systems play an important role. In this paper, we consider sharp bounds for the mean residual life function of a k-out-of-n system consisting of n identical components with independent lifetimes having a common distribution function F, measured in location and scale units of the residual life random variable X _t  = (X−t|X > t). We characterize the probability distributions for which the bounds are attained. We also evaluate the so obtained bounds numerically for various choices of k and n.     

An outlier test for linear processes — II. Large contamination

In Flak/Schmid (1993) an outlier test for linear processes was introduced. The test statistic bases on a comparison of each observation with a one-step predictor. It was assumed that an upper bound for the total number of outlierss _n is known, wheren denotes the sample size. The asymptotic distribution of the test statistic was derived under the assumption thats _n/n → 0 ands _n → ∞ asn → ∞. This note deals with the asymptotic behaviour of this quantity, ifs _n/n →p ₀ ∈ (0, 1).     

Performance Measures in Dose-Finding Experiments

In the first phase of pharmaceutical development, and assuming that the probability of positive response increases with dose, the main statistical goal is to estimate a percentile of the dose–response function for a given target value $\mathrm{\Gamma }$. We compare the Maximum Likelihood and centred isotonic regression estimators of the target dose and we discuss several performance criteria to assess inferential precision, the amount of toxicity exposure and the trade-off between them for a set of some exemplary adaptive designs. We compare these designs using graphical tools. Several scenarios are considered using simulation, including the use of several start-up rules, the change of slope of the dose-toxicity function at the target dose and also different theoretical models, as logistic, normal or skew-normal distribution functions.     

Work and Welfare in Economics:

Abstract . Today's conventional economics typically ignores the impact of alternative forms of work organization upon the welfare of the worker. In effect, its methodology is concerned with the welfare of the individual as a consumer, but not with the welfare of the individual as a worker. Hence, welfare conclusions of economics are subject to challenge on grounds of being incomplete. Whether the worker is alienated or achieves self-fulfillment, etc., stands in no necessary relationship to either the formal lines of enterprise ownership, political ideology or form of economic system. Questions of authority and power in work organizations and the workplace conditions affecting the worker on the job transcend them.     

Exact local Whittle estimation of fractionally cointegrated systems

Semiparametric estimation of a bivariate fractionally cointegrated system is considered. We propose a two-step procedure that accommodates both (asymptotically) stationary (δ<1/2)$(\delta <1/2)$ and nonstationary (δ≥1/2)$(\delta \ge 1/2)$ stochastic trend and/or equilibrium error. A tapered version of the local Whittle estimator of Robinson (2008) is used as the first-stage estimator, and the second-stage estimator employs the exact local Whittle approach of Shimotsu and Phillips (2005). The consistency and asymptotic distribution of the two-step estimator are derived. The estimator of the memory parameters has the same Gaussian asymptotic distribution in both the stationary and the nonstationary case. The convergence rate and the asymptotic distribution of the estimator of the cointegrating vector are affected by the difference between the memory parameters. Further, the estimator has a Gaussian asymptotic distribution when the difference between the memory parameters is less than 1/2.     

Criterion-robust optimal product designs for discrimination between nested response surface models

Consider the problem of discriminating between two rival response surface models and estimating parameters in the identified model. To construct designs serving for both model discrimination and parameter estimation, the M _γ-optimality criterion, which puts weight γ (0≤γ≤1) for model discrimination and 1 − γ for parameter estimation, is adopted. The corresponding M _γ-optimal product design is explicitly derived in terms of canonical moments. With the application of the maximin principle on the M _γ-efficiency of any M _γ'-optimal product design, a criterion-robust optimal product design is proposed.     

Assessment of Interjudge Reliability in the Open-Ended Questions Coding Process

In the process of coding open-ended questions, the evaluation of interjudge reliability is a critical issue. In this paper, using real data, the behavior of three coefficients of reliability among coders, Cohen’s K, Krippendorff’s α and Perreault and Leigh’s I _r are patterned, in terms of the number of judges involved and the categories of answer defined. The outcome underlines the importance of both variables in the valuations of interjudge reliability, as well as the higher adequacy of Perreault and Leigh’s I _r and Krippendorff’s α for marketing and opinion research.     

Irrational Expectations, Unclearing Markets and a Business Cycle That Won't Go Away: The Recent School of New Classical Economists Comes a Cropper on Basic Economic Facts

Abstract . The assumptions and conclusions of New Classical Macroeconomics (NCM) are critically examined. NCM grew out of the alleged failure of the Keynesian school to deal with the problems of stagflation of the 1970s. The two fundamental ideas of the NCM are the rational expectations hypothesis and the theory of instantaneous market clearing. According to the NCM, fiscal and monetary policies will achieve desired results if they are unanticipated. Business cycles are thought to be results of imperfect information on the part of rational agents (people). The NCM has been severely criticized by such prominent economists as Arrow, Tobin and Thurow.     

Biases,variances and covariances of raking ratio estimators for marginal and cell totals and averages of observed characteristics

Summary On the basis of a simple random sample from a population, on which a cross-classification is defined with known marginal frequenciesN _i. andN _.j , one wishes to estimate the cell frequenciesN _ij , as well as cell totalsY _ij , marginal totalsY _i. andY _.j , and the grand totalY for characteristics measured on the units. Various authors have discussed so-called raking ratio estimators, which are built up from the estimated cell values by addition. They have given the bias and variance of this estimator ofY. This paper derives biases, variances and covariances for the corresponding estimators of the cell and marginal totals and of the corresponding marginal averages.