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Summary This paper discusses the statistical issues that arise in conducting an economic damages analysis in the context of a litigation matter involving copyrights. Calculating damages in copyright cases turns out to be a natural application for econometric modelling methods. Surprisingly, elementary statistical issues can be a source of significant debate between the experts in such matters. In this paper, we present a case study and illustrate how issues such as interpretation of p-values and what “rejection of the null hypothesis” really “means” in such matters. Resume Cet article discute les questions statistiques qui se posent dans la conduite d'une analyse des dommageseconomiques dans le contexte d'un litige concernant les copyrights. Le calcul des dommages dans les cas de copyright s'avere etre une application naturelle des methodes de modelisation econometrique. Curieusement, des questions statistiques elementaires peuvent etre la source de debat significatif entre experts sur de telles questions. Dans cet article, nous pesentons une etude de cas et illustrons la signification reelle de questions telles que l'interpretation des p-valeurs et le rejet de l'hypothese de nullite.

In the 1990s three decisions of the United States Supreme Court raised standards for admissibility of scientific and special knowledge testimony in Federal trials. Many states have adopted comparable standards. Expert economic testimony that seeks to prove facts from statistical generalizations has received considerable scrutiny in litigation. This article focuses on the nitty-gritty of performing regression studies that can meet the new standards for admissibility. The article redefines chance outliers in terms of tail probabilities of distributions. Tests for presence of outliers produced by anomalous factors are specified in terms of number of diagnosed outliers and waiting-times of their occurrence.

This chapter presents an exposition of the Generalized Fechner–Thurstone (GFT) direct utility function, the system of demand functions derived from it, other systems of demand functions from which it can be derived, and its purpose and the econometric circumstances that motivated its original development. Its use in econometrics is demonstrated by an application to household consumer survey data which explores the relationship between prices, on the one hand, and expected exogenous preference changers such as household size, schooling of heads of household, and other social factors, on the other.

The purpose of this paper is to specify a functional form of a Lorenz curve which allows us to examine an aspect of the observed income graduation which has not previously been analyzed. We demonstrate that the form of the Lorenz curve specified satisfied a Riccati differential equation and the logarithmic derivative satisfies a Bernoulli differential equation which allows us to discuss the notion of what we call the Mobility function. This function conveys information about the relative difficulty of moving up the personal income distribution. We estimate various points along this function for the years 1977 and 1983.

This paper studies alternative cost-of-living indexes derived from the generalized Fechner-Thurstone (GFT) utility form, their use in contracts for cost-of-living adjustments (COLAs), and the resulting effect of choice of index on the distribution of real income. The indexes and their distributional effects are compared to the officially reported Consumer Price Index (CPI) and a CPI computed from the same data set used to compute the GFT indexes. It is found that the choice of index used in adjustment clauses in contracts has an impact on the distribution of real income of the group. As an example, the U.S. federal government schedule of wages and salaries is adjusted from 1981 through 1984 by all of the indexes reported here. Use of alternative indexes illuminates the normative assumptions regarding the relative importance of different income strata (among other things) implicit in any public practice of pegging COLAs to a single form of price index.

A production system modeling tool is developed that implements recent work on autoregressive and endogenous stochastic production technologies associated with generalized Fechner-Thurstone (GFT) optimizing functions. A GFT-class production system is used to evaluate the empirical support for technology specifications inherent in the neoclassical theoretic structure of an agricultural production region. Little likelihood support is found for zero serial correlation, elimination of systematic technology changers from the production system, strict neoclassical production technologies, Hicks-neutral technical change, or zero homogenous factor demand functions.

The purpose of this paper is to present several descriptive approximations of empirical Lorenz curves. Each of these hypothetical forms is less restrictive than those considered before. We compare these alternative forms by goodness of fit, F -tests of nested forms, and measurement of the Gini coefficient.

Whenever a neoclassical direct utility function is in close (even perfect) agreement with consumer behavior data, there is always an alternative direct utility function that agrees at least as closely with the same data. Existence of this equally well (if not better) fitting alternative to such a neoclassical direct utility function has considerable significance for the rational conduct of potential problem analysis in the policymaking arena. [We shall give an important example later in this note.] However the nonuniqueness of the neoclassical utility function on empirical data is rarely mentioned in the literature of economic theory, it appears to be little understood among economists generally, and most doctoral students are never told about it in advanced economic theory courses.

In abstract mathematics the Gini coefficient of concentration is one of several diverse measures of the degree of the concentration of a purely mathematical, or uninterpreted, distribution function. Camilo Dagum has provided a thoughtful perspective on analyzing the Gini that is unique among modern economists due to his personal relationship with Gini. Camilo does not have to “guess” what Gini meant in interpreting the Gini in a given context, because he actually worked side by side with Gini. A review of Camilo’s Bibliography (at the beginning of this set of essays written in his honor) reveals the richness, diversity and dept of Camilo’s work on that subject matter. We are pleased to present this essay on the Gini in Camilo’s honor.

This study is concerned with the effect of an identifiability pretest on the locations and shapes of conditional distributions of structural coefficient estimators in a simultaneous equations model. We examine whether there are important cases in which the identifiability test statistic and (correctly) restricted structural coefficient estimators such as 2SLS and 3SLS are “approximately” statistically independent over a broad range of Type I error levels of for the test statistic. The results of the Monte Carlo experiments based on the Klein model I are not conclusive, though they tend to support approximate independence in most cases.

This paper presents a new class of weighted geometric mean inequality measures. This class allows us to make explicit the latent weighting other well-known inequality measures are giving to various portions of the observed income graduations under scrutiny. Since policymakers rely on measures such as the Gini coefficient to convey information to them about the level of inequality, knowledge of such implicit weightings is important.

This article examines the sensitivity of the cost of living to some aspects of price changes and income changes that cannot be detected by Laspeyres indexes like the CPI-U or CPI-W. Effects of price-induced and income-induced changes in consumers tastes on the cost of living in the United States from 1947 to 1981 are estimated and found to be generally substantial.

In this article some leading results of a mathematical investigation of exact finite sample distributions of GCL estimators are given. These results pertain to the distributions of estimators of coefficients appearing in econometric systems of three structural equations. The results show that the general forms of exact distributions derived for coefficient estimators in two-equation systems re-appear in the corresponding cases of three equations systems.

As is true of any statistical application, testing econometric statistical hypotheses involves constructing critical regions with prescribed probabilities of Type I error and determining probabilities of Type II error under alternative hypotheses. Such constructions and determinations presuppose knowledge of exact statistical distribution functions of econometric estimators and test statistics either directly, or indirectly, as in the case where a statistical distribution function that approximates the exact distribution with known margin of error is used. If this requisite information is not available, econometric statistical inference remains guesswork. Partly because of the complicated nature of systems of simultaneous econometric structural equations and the large numbers of structural constants required to characterize distribution functions of econometric statistics, however, only a few exact marginal distributions of econometric estimators and test statistics have been extracted so far. Th...

In a recent paper, Hayes, Molina and Slottje (1988) examined the question of preference variation across North America. As the economy of the United States becomes a more open economy and less immune to fluctuations in international markets, the impact of relative price changes of foreign commodities on domestic economic well-being will be of increasing interest. Earlier studies have focused on the welfare impact of foreign price changes (cf Thursby (1981)). In this chapter, potential secondary utility effects of foreign prices are examined, the chapter follows Hayes, Molina and Slottje (1988).

Marshall long ago noted the phenomenon of past consumption being highly correlated with current consumption. If “habit” was indeed a major determinant of current consumption behavior, then the neo-classical theory of utility maximization should take it into account. A rigorous incorporation of habit formation into consumer theory began with the work of Gorman (1967). Pollak (1976, 1977) laid out the theoretical conditions that needed to be satisfied in order for “habit persistence” to be consistent with the utility maximizing model of consumer behavior.

In the last chapter we showed explicitly how the GFT-direct utility function yields empirically testable hypotheses. Since Cournot, Dupuit and Gossen first laid out what evolved into the modern theory of consumer demand (predicated on the concept of individual utility maximization) a hundred and fifty years ago, virtually hundreds of articles have been written attempting to explicate and measure the theory cf. Stigler (1954). Among the modern contributors, Stone (1954), Houthakker (1960), Theil (1967), Christensen, Jorgenson and Lau (1975), Deaton and Muellbauer (1980a) and Basmann, Molina and Slottje (1983) have all introduced explicit demand functions to test the theory. Some have based their demand systems on explicit utility functions, some have not.

This chapter examines the sensitivity of the cost of living to some aspects of price changes and income changes that cannot be detected by Laspeyres indexes such as the CPI-U and CPI-W. Although its content is confined to positive economic analysis, the article does cast light on normative choices in welfare policy. Formation of practical strategies in the negotiation of escalator clauses in private sector wage contracts involves consideration of both normative values and positive descriptions of the real environment. The same is true of policy choices in the political arena, for instance in the determination of cost-of-living adjustments (COLAs) in pensions and transfer payments. The price and income sensitivities of the cost of living, expressed as elasticities, are used to determine the size of COLAs required to keep real incomes of recipients constant.

1 Introduction.- 2 The GFT Utility Function.- 3 Estimating the GFT Form.- 4 The GFT and Alternative Forms.- 5 The True Cost-of-Living Concept.- 6 Cross Country Comparisons.- 7 Testing for Habit Persistence.- 8 Concluding Remarks.- A The Five Commodity Groups.- B The Eleven Commodity Groups.

A theory of consumer demand with variable preferences. The assumption that the individual consumer has a unique ordinal utility index function is replaced by the assumption that he has a family of ordinal utility functions; advertising expenditures by the sellers of commodities are assumed to determine which one of these ordinal utility functions is to be maximized. From these assumptions are derived a number of theoretical relations which measurements defining advertising elasticities of demand must satisfy. The relations involving shifts in demand and advertising elasticities of demand are shown to be analogues of the theorems of consumer demand under fixed preferences.

Samuelson, in his Foundations of Economic Analysis (1947), credits Walras with having shown many years before that it is possible to modify utility analysis so as to take account of the peculiar properties of money; (Samuelson, 1947b, p. 118).The first part of this chapter is adapted in part from Basmann, Molina and Slottje (1987). The latter exposition follows Basmann, Molina and Slottje (1984a). In response to Walras’ critics who feared “that there was something viciously circular in assuming the existence of prices and of a ‘value for money’ in the midst of the process by which that value was to be determined” Samuelson sought to clear up such misconceptions, by deriving the consumer’s demand function for holding of money from a utility function subject to a linear budget constraint in which the price of “gold”1 and the rate of interest, as well as commodity prices and total expenditure appear as parameters; (Samuelson, 1947b, pp. 119–121). Samuelson introduced commodity prices and the price of “gold” into the consumer’s ordinal direct utility function U(X; p) as parameters.2 Apart from the usual restrictions on fixed-preference utility functions, only homogeneity of degree zero in all prices was imposed. Even without an explicit form of a direct utility function that restriction is sufficient to imply the meaningful, refutable hypothesis that the demand for (holding) money has unitary own-price elasticity; (Samuelson, 1947b, p. 121).

If two simultaneous equations economic models, each purporting to explain the same endogenous variable in terms of the same exogenous variable differ only in this respect, that one is in the form of an ‘interdependent’ representation and the other is an ‘explicit causal chain,’ then the question whether one is a more accurate representation of economic reality than the other cannot even in principle be settled by appeal to observations. The failure of proponents of ‘explicit causal chains’ to appreciate the significance of the foregoing theorem has led to the proposal of a remarkable interpretation of unfavorable outcomes of statistical tests of econometric hypotheses (which is mentioned in Section 3.2).

The Strotz-Wold "Reply," however, penetrates to the heart of the issue, almost, and it will probably be illuminating to make a rejoinder. To begin with I should like to say that they are justified in taking exception to the unfortunate wording of the headnote. Though, when applied to the sequence of recipes given out by Wold, my remarks do not lack for verisimilitude, they are certainly not true to the letter of the Strotz-Wold article, and I should have taken pains not to convey the impression that I thought they were.2 Accepting their just remonstrance, I turn to the text of my article. The main contention of my paper was that the classical scientific notion of causality (not, however, the doctrine of "cause" and "effect") 3 is adequate to rationalize the construction of non-triangular or "interdependent" mechanical models in economics; that employment of the classical notion in the case of non-triangular systems neither leads to paradox nor calls for novel categories of causality, e.g., circular causality, bi-causality, vector causality

In a recent article appearing in this journal Turner and Stevens [1959] have presented an excellent discussion of regression analysis of causal paths based on the early work of Sewall Wright and others. The authors note that considerable work on the treatment of multiple equations has also been done by econometricians. (See the papers by Haavelmo [1943, 1944], Koopmans and Reiers0l 1950].) The purpose of the present note is to make known to biologists and biometricians several methods of genieralized linear estimation of structural parameters not yet widely known outside of econometrics, in particular the leastvariance difference method. The latter method, in two different forms, has been introduced into the econometric literature by Theil [1953] and the present author [1957]; but the principle on which it is based and, indeed, the mathematical technique itself have been known for some considerable time in the Theory of Errors, the principle having been laid down and the technique fully adumbrated by Gauss [182123j. This principle, in Gauss's words, asserts that "The most plausible value of a quantity that is a given function of the unknown quantities (i.e. the parameters) of the problem is found by one's substituting for the latter their most plausible values as determined by the Method of Least Squares." (Gauss [1823], pp. 34ff., pp. 102-3.) This principle foreshadows the well-known modern theorem about the invariance of maximum-likelihood estimators. The technique of least-variance difference estimation can be formulated exactly as Aitken's [1935] generalization of Gauss's method of treating independent observations of unequal precision (Gauss [1809], p. 214) to the case of interdependent observations. The plan of this note is as follows: Section 2 contains a discussion of some logical features of causal