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).     

Tax competition,uniform assessment,and the benefit principle

In previous discussions it has been argued that tax competition between local governments results in a tax burden on business that is less than the cost of public services for business and in suboptimal levels of public expenditures for residents. However, this conclusion has never been substantiated by a full theoretical treatment. Here a theoretical model of tax competition is developed between metropolitan areas, with labor perfectly immobile and two local public goods, one for residents and one for business. For “plausible” parameter values, numerical solutions of the optimality conditions are computed by means of a nonlinear programming algorithm.     

Restricted maximum likelihood estimation under Eisenhart model Ill

For a balanced two-way mixed model, the maximum likelihood (ML) and restricted ML (REML) estimators of the variance components were obtained and compared under the non-negativity requirements of the variance components by L ee and K apadia (1984). In this note, for a mixed (random blocks) incomplete block model, explicit forms for the REML estimators of variance components are obtained. They are always non-negative and have smaller mean squared error (MSE) than the analysis of variance (AOV) estimators. The asymptotic sampling variances of the maximum likelihood (ML) estimators and the REML estimators are compared and the balanced incomplete block design (BIBD) is considered as a special case. The ML estimators are shown to have smaller asymptotic variances than the REML estimators, but a numerical result in the randomized complete block design (RCBD) demonstrated that the performances of the REML and ML estimators are not much different in the MSE sense.     

On bivariate generalized binomial and negative binomial distributions

The present paper deals with two types of generalized general binomial (binomial or negative binomial) distributions: (i) a univariate general binomial generalized by a bivariate distribution and (ii) a bivariate general binomial generalized by two independent univariate distributions. The probabilities, moments, conditional distributions and regression functions for these distributions are obtained in terms of bipartitional polynomials. Moreover recurrence relations for the probabilities and moments, independent of the bipartitional polynomials, are given. Finally these general results are applied to the (i) Binomial-Bivariate Poisson and (ii) Bivariate Binomial-Poissons distributions.     

The micro-foundations of intertemporal price discrimination

Summary. This paper investigates the optimality of intertemporal price discrimination for a durable-good monopoly in a model where infinitely-lived households face an intertemporal budget constraint, and consume both durable goods and non-durable goods. We prove that the optimal price of the durable good is not constant, and may decrease or increase over time. Some households may choose to purchase the durable good at a later date, and pay lower or higher prices, since the gain in discounted utility of consuming more of the non-durable good more than compensates for the loss in utility from delaying the consumption of the durable good.Received: 12 March 2004, Revised: 7 January 2005, JEL Classification Numbers: D40, D42, D91.I would like to thank C.D. Aliprantis, the Editor, and an anonymous referee for their generous advice, and constructive comments and suggestions. I have also enjoyed discussions with John Quah on the subject. Research support from the Wharton-SMU Research Centre, Singapore Management University, is gratefully acknowledged.     

Revealed preference and differentiable demand

Summary. We prove that, for finitely many demand observations, the Strong Axiom of Revealed Preference tests not only the existence of a strictly concave, strictly monotone and continuous utility generator, but also one that generates an infinitely differentiable demand function. Our results extend those of previous related results (Matzkin and Richter, 1991; Chiappori and Rochet, 1987), yielding differentiable demand functions but without requiring differentiable utility functions.Received: 1 November 2001, Revised: 5 February 2004, JEL Classification Numbers: D11, D12. Correspondence to: Kam-Chau WongThis is a much revised version of Lee and Wong (2001). We are grateful to the Referee for valuable suggestions. We also thank Professor Marcel K. Richter for his comments.     

Deposit insurance and bank regulation in a monetary economy: a general equilibrium exposition

Summary. It is commonly argued that poorly designed banking system safety nets are largely to blame for the frequency and severity of modern banking crises. For example, underpriced deposit insurance and/or low reserve requirements are often viewed as factors that encourage risk-taking by banks. In this paper, we study the effects of three policy variables: deposit insurance premia, reserve requirements and the way in which the costs of bank bailouts are financed. We show that when deposit insurance premia are low, the monetization of bank bailout costs may not be more inflationary than financing these costs out of general revenue. This is because, while monetizing the costs increases the inflation tax rate, higher levels of general taxation reduce savings, deposits, bank reserves, and the inflation tax base. Increasing the inflation tax rate obviously raises inflation, but so does an erosion of the inflation tax base. We also find that low deposit insurance premia or low reserve requirements may not be associated with a high rate of bank failure.Received: 2 January 2002, Revised: 1 March 2003JEL Classification Numbers: D5, E5, G1.B. D. Smith: Sadly, our co-author, colleague and dear friend, Bruce D. Smith, died on July 9, 2002.     

Pricing access in network competition

We compare various access pricing rules in the two-way access model. We show that the Generalized Efficient Component Pricing Rule (TECPR) leads to a lower equilibrium price than does the Efficient Component Pricing Rule, (ECPR) marginal cost pricing, (MCP) and any non-negative fixed access charges.