A note on the exact transformation associated with the first-order moving average process

Exact analytical expressions for the transformation that can be used to transform a generalized regression problem into a simple regression problem are available for a variety of models. Such is the case, for instance, for purely heteroscedastic models, for the first-order Markov process and for error components models. For the first-order moving average process, on the other hand, the exact transformation has not yet been produced. This gap is filled in the present note.Implications for estimation and prediction are also considered.     

Competition,regulation and bribery: A further note

In this note we extend the analysis of Beck and Maher (1989) concerning the effects of discriminatory anti-bribery regulation. We argue that their approaches are challengeable due to an additional assumption that is most likely inconsistent with the benchmark model. Upon discarding the controversial assumption, we have an asymmetric bribery game. The corresponding Bayesian Nash equilibrium is nonetheless possessed with the properties described in Beck and Maher, despite the fact that their approaches may be incorrect.     

A further note on arrow's impossibility theorem

For arbitrary measure spaces of agents we investigate the existence of social welfare functions which fulfill a suitable non-dictatorship axiom; it turns out that there is an essential difference between finite and σ-finite but infinite measure spaces. Furthermore the condition of universal domain of social welfare functions is weakened.     

A further note on the structure of gas distribution costs in urban areas

This note re-examines the issue of functional form selection in estimating the relationship between gas distribution costs and market and density variables. The study by [Guldmann, 1983], where only linear and log-linear forms were considered, is expanded by using a general functional form based on the Box-Cox transformation. The maximum-likelihood estimated forms turn out to be different from the log-linear ones previously selected, and their implications for economies of scale and density are discussed.     

A Bayesian approach to imposing curvature on distance functions

The estimated parameters of output distance functions frequently violate the monotonicity, quasi-convexity and convexity constraints implied by economic theory, leading to estimated elasticities and shadow prices that are incorrectly signed, and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels. We show how a Bayesian approach can be used to impose these constraints on the parameters of a translog output distance function. Implementing the approach involves the use of a Gibbs sampler with data augmentation. A Metropolis–Hastings algorithm is also used within the Gibbs to simulate observations from truncated pdfs. Our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time-invariant. Two models—a fixed effects model and a random effects model—are developed and applied to panel data on 17 European railways. We observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed.     

A note on the role of the average cost curve in the neoclassical theory of the firm

A number of influential authors have argued that the long-run average cost curve has only a limited role in the theory of the firm. This note examines this claim in more detail. It argues that the curve has an important role in determining long-run equilibrium as it provides an important ‘signal’ to agents in the capital and product market about the extent to which an industry is in disequilibrium. The effect of removing the certainty assumption is then examined and it is argued that the average cost curve is an important input in the assessment of operating risk.     

A further note on the asymptotic efficiency of friedman’s x r 2 -test

Summary For independently distributed error components, the asymptotic relative efficiency (A.R.E.) ofFriedman’sx _r ² -tests with respect to the classical analysis of variance test has been studied byElteren andNoether andSen [1967]. The present note extends these results to the case of correlated errors arising in some random-effects or mixed-effects models. Work supported by the U.S. Army Research Office, Durham, Grant DA-ARO-D-31-124-G 746.     

Metropolitan density functions : A Further exploration

The application of mathematical functions to population density data within metropolitan areas has become a well-established analytical procedure. The more important functions that have been previously employed in this connection are reviewed, and two additional functional forms are suggested. The proposed functions, together with the earlier ones, are evaluated in terms of their ability to describe actual density patterns, as well as their accuracy in characterizing certain features of metropolitan spatial structure. The evaluation is undertaken in relation to two metropolitan areas of the United Kingdom. While these both possess certain distinctive features, they conform in many respects to metropolitan areas in other western nations.     

A note on the upper bound for the distance in total variation between the binomal and the Poisson distribution

Abstract  The total variation distance between the binomial B ( n, p ) distribution and the Poisson P ( np ) distribution is smaller than 2 ^1/2 p (1- p )^-1/2 according to V ERVAAT [4], [5]. We shall sharpen this inequality by using a result due to K EMPERMAN [1], C SISZÁR [2] and K ULLBACK [3].     

Quantile-locating functions and the distance between the mean and quantiles

Given a random variable X with finite mean, for each 0 < p < 1, a new sharp bound is found on the distance between a p -quantile of X and its mean in terms of the central absolute first moment of X . The new bounds strengthen the fact that the mean of X is within one standard deviation of any of its medians, as well as a recent quantile-generalization of this fact by O'Cinneide.     

A note on Balestra's (1980) approximate estimator for the first-order moving average process

An approximate procedure, based on Balestra's stated assumptions, is developed. The new method is shown to have superior performance to the approximate procedure developed by Balestra for small sample sizes when the value of the moving average parameter, C, is between zero and 0.50. For C in this region, the new method is also shown to be nearly as good as the exact procedure.     

A bias in estimating urban population density functions

This paper demonstrates that because of the rules used to delineate census tracts, unweighted estimation of an urban population density function using census tract observations leads to a severe upward bias in the estimated function. A weighted estimation procedure which leads to an unbiased estimate is proposed. The paper also points out that if one computes the integral of an unbiased estimate of a density function over the area of a city, that integral is not necessarily an unbiased estimate of total population. The paper thus explains the “disturbing” empirical results concerning density functions reported by McDonald and Bowman.     

Melbourne: Population density; distance; the relationship

The analysis of two earlier writers is replicated using a data base pertaining to Melbourne, Australia, for the period 1901 to 1976. Several alternative functional forms of the population density functions are tested to determine comparative goodness of fit to the data. Population estimates are obtained and contrasted to actual population figures, and finally density functions incorporating time as an argument are estimated.