Robert A. Pollak

On Second-Best National Saving and Game-Equilibrium Growth

This chapter highlights the question whether second-best saving is greater or smaller than first-best saving when given future saving is non-optimal from the standpoint of the present generation. The chapter presents the postulation that all generations expect each succeeding generation to choose the saving ratio that is second-best in its eyes. This somewhat game-theoretic model leads to the concept of an equilibrium sequence of saving-income ratios having the property that no generation acting alone can do better and all generations act so as to warrant the expectations of the future saving ratios. The chapter presents a comparison of this equilibrium and the first-best optimum. The concept and calculation of the second-best optimum is of interest even if that analysis does not explain actual national saving because society as a whole has no notion of such an optimum.

Demographic Variables in Demand Analysis

In this paper [the authors discuss] five procedures for incorporating demographic variables into theoretically plausible demand systems: translating scaling and the Gorman reverse Gorman and implicit Prais-Houthakker procedures.... These five procedures are used to incorporate a single demographic variable--the number of children in a household--into the generalized CES demand system using household budget data for the United Kingdom for the period 1966-1972 (EXCERPT)

Conditional Demand Functions and Consumption Theory

Introduction, 60. — I. Conditional demand functions, 61. — II. Conditional demand functions and ordinary demand functions, 64. — III. A new decomposition of the cross price derivatives, 65. — IV. Consumer behavior under straight rationing, 70. — V. Hicksian aggregation, 74. — VI. The Le Chatelier Principle and beyond, 75.

Family Structure and Children's Educational Outcomes: Blended Families, Stylized Facts, and Descriptive Regressions

This article adds to the growing literature describing correlations between children’s educational outcomes and family structure. Popular discussions have focused on the distinction between two-parent families and single-parent families. This article shows that educational outcomes for both types of children in blended families—stepchildren and their half-siblings who are the joint children of both parents—are similar to each other and substantially worse than outcomes for children reared in traditional nuclear families. We conclude that as a description of the data, the crucial distinction is between children reared in traditional nuclear families (i.e., families in which all children are the joint children of both parents) and children reared in other family structures (e.g., single-parent families or blended families). We then turn from “stylized facts” (i.e., simple correlations) that control only for family structure to “descriptive regressions” that control for other variables such as family income. When controls for other variables are introduced, the relationship between family structure and children’s educational outcomes weakens substantially and is often statistically insignificant.

The likelihood dominance criterion: A new approach to model selection

Abstract The dominance ordering and the LDC provide a new approach to model selection. The dominance ordering is described in terms of a fictive experiment in which the two competing hypotheses are nested in a composite. If estimating the composite would lead to accepting one hypothesis and rejecting the other, then which would be accepted and which rejected is determined by the two adjusted likelihood values and does not require estimating the composite, although it does require specifying its parametric size. The LDC generalizes the dominance ordering by considering a range of admissible composite parametric sizes. This range will usually include all sizes of practical interest.

Habit formation and long-run utility functions☆

Abstract This paper extends the work on habit formation of Pollak [Habit formation and dynamic demand functions. J. Polit. Econ. (1970)] and provides a critical counterexample to a conjecture of von Weizsacker [Notes on endogenous changes of tastes, J. Econ. Theory (1971)] concerning the existence of a “long-run utility function.“ A linear specification of habit formation is applied to a general system of demand functions with linear Engel curves. It is shown that there exists a utility function which rationalizes the long-run demand functions if and only if they are the steady-state solution to a system of short-run demand functions generated by an additive utility function.

Do Parents Favor Boys

In an optimizing model of parental allocation systematic differences in human capital investments betwen the sexes may originate in at least 3 ways. 1) Parents may respond to expected gender wage differentials. 2) Parents may respond to systematic differences by gender in the price of human capital investments. 3) Parental preferences may favor girls or boys in the sense that they value identical outcomes at the same cost more highly for one sex than for the other. This paper analyzes the role of parental preferences in general and unequal concern in particular in the allocation of human capital investments among children. The authors generalize their earlier model of the human capital investments among children to incorporate the possibility that the returns to such investments may include not only the childs own ecpected earnings but also the expected earnings of his or her spouse. Thus the model assumes that parents may value returns that accrue trough the marriage market as well as through education. The relevant returns to education may include marrying a spouse with higher expected earnings. The empirical analysis indicates that gender wage differentials like endowment differentials are mildly reinforced by the parental allocation of human capital investments. Marriage market outcomes are significant determinants of the allocation of human capital investments among children. There is no evidence that parental preferences favor boys; this study shows that parental preferences either exhibit equal concern or slightly favor gils.

Family Resources, Family Size, and Access to Financing for College Education

Unequal access to financing for education may be an important source of educational differences. We develop a model relating sib schooling and earnings similarities to sibship size with and without equal access and estimate it for the education of veterans, for whom the GI Bill assured equal access, and for their children, who had no such government assistance. We find an inverse relationship between sibship size and sib schooling and earnings similarities for the children, but not for the veterans; we conclude that, in the absence of equal access policies, unequal access is an important source of educational differences.

The social cost of living index

Abstract Household cost of living indexes reflect household preferences; analogous indexes for groups of households require a corresponding concept of group preferences. In this paper I investigate the ‘social cost of living index’, a group index based on the Bergson-Samuelson social welfare function. I first define the index and examine its properties under the assumption that the investigator constructing it expresses his distributional judgments in an explicit Bergson- Samuelson social welfare function; I then examine the ‘maximizing society’ and the ‘independent society’, two cases in which the index can be constructed from the information contained in the market demand functions. In these two cases a Laspeyres index (i.e. the fixed weight index based on the reference consumption pattern) is an upper bound on the exact social cost of living index. In general, however, the assumptions required to place bounds on the social cost of living index are much more likely to be satisfied than those required to place analogous bounds on a households cost of living index.

Conditional Demand Functions and the Implications of Separable Utility

Most contributions to demand theory can be divided into two distinct categories. One consists of studies of the foundations of the theory; these are usually concerned with weakening the fundamental axioms to obtain greater generality. The other consists of studies which impose strong restrictions on either preferences or demand functions and investigate the implied restrictions on the other; these sacrifice generality to obtain specific results. In the former category are investigations of the conditions under which preferences can be represented by real valued, continuous utility functions and of the conditions under which demand functions can be defined in the absence of such representability. Examples include Chipman [1], Rader [14], Debreu [2], Sonnenschein [17] and Richter [15]. The latter category includes investigations of the demand functions arising from specific utility functions (e.g., Wegge, 22), of self-dual preference orderings [Houthakker, 7] and, perhaps most prominently, of separable utility functions [Strotz, 19; 20; Gorman, 5; Frisch, 3; Houthakker, 6; Sono, 18; Pearce, 10; 11; Goldman and Uzawa, 4]. The purpose of this paper is to derive and explain the implications for consumer behavior of the three principal separability hypotheses: the utility tree, block additivity and additivity.l Although most of the results