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Book ChapterDOI

A Class of Dynamic Demand Systems

01 Jan 1989-Research Papers in Economics (Springer, Dordrecht)-pp 93-116

AbstractThis paper derives closed-form solutions for the total consumption-expenditure function (i.e., aggregate consumption function), the savings function and the demand functions from a nonstationary intertemporal utility-maximization problem under uncertainty for a class of demand systems, including the linear expenditure system (LES) from the Klein-Rubin-Samuelson (KRS) utility function, the generalized linear expenditure systems (GLES) from the CES and S-branch-tree utility functions, the Almost Ideal Demand System (AIDS) from the PIGLOG class of preferences, and the indirect addilog demand system (IADS). We do so by following Hicks’ and Tinmer’s method of maximizing a discounted utility function subject to expected constraints rather than the more fashionable method of maximizing an expected discounted utility function subject to stochastic constraints. Furthermore, the preferences are allowed to vary with the time period. Theoretical analyses for these systems are also given in this paper.

Topics: Discounted utility (65%), Inverse demand function (61%), Almost ideal demand system (61%), Demand curve (57%) more

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Munich Personal RePEc Archive
A Class of Dynamic Demand Systems
Tian, Guoqiang and Chipman, John S.
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MPRA Paper No. 41387, posted 17 Sep 2012 13:35 UTC

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Journal ArticleDOI
Abstract: Introduction References and Suggested Readings PART I REAL DYNAMIC MACROECONOMIC MODELS 1. Dynamic Programming A General Intertemporal Problem A Recursive Problem Bellman's Equations Nonstochastic Examples The Optimal Linear Regulator Problem Stochastic Control Problems Examples of Stochastic Control Problems The Stochastic Linear Optimal Regulator Problem Dynamic Programming and Lucas's Critique Dynamic Games and the Time Inconsistency Phenomenon Conclusions Exercises References and Suggested Readings 2. Search Nonnegative Random Variables Stigler's Model of Search Sequential Search for the Lowest Price Mean-Preserving Spreads Increases in Risk and the Reservation Price Intertemporal Job Search Waiting Times Firing Jovanovic's Matching Model Conclusions Exercises References and Suggested Readings 3. Asset Prices and Consumption Hall's Random Walk Theory of Consumption The Random Walk Theory of Stock Prices Lucas's Model of Asset Prices Mehra and Prescott's Finite-State Version of Lucas's Model Asset Pricing More Generally The Modigliani-Miller Theorem Government Debt and the Ricardian Proposition Remarks on Testing and Estimation Conclusions Exercises References and Suggested Readings PART II MONETARY ECONOMICS AND GOVERNMENT FINANCE 4. Currency in the Utility Function The Price of Inconvertible Government Currency in Lucas's Tree Model Issues and Models in Monetary Economics Government Debt in the Utility Function Government Currency in the Utility Function Seignorage and the Optimum Quantity of Currency A Neutrality Proposition Conclusions References and Suggested Readings 5. Cash-in-Advance Models A One-Country Model Fisher Equations Inflation-Indexed Government Debt Interactions of Monetary and Fiscal Policies Interest on Reserves A Two-Country Model Exchange Rate Indeterminacy Conclusions Exercises References and Suggested Readings 6. Credit and Currency with Long-Lived Agents The Physical Setup Optimal Allocations Competitive Equilibrium A Digression on the Balances of Trade and Payments The Ricardian Doctrine about Taxes and Government Debt The Model with Valued Currency and No Private Debt An Interventionist Optimal Monetary Equilibrium Townsend's \"Turnpike\" Interpretation Conclusions Exercises References and Suggested Readings 7. Credit and Currency with Overlapping Generations The Overlapping-Generations Model The Ricardian Doctrine about Taxes and Government Debt Again A Ricardian Proposition Currency, Bonds, and Open-Market Operations Computing Equilibria Interpretations as Currency Equilibria Optimality Four Examples on Inflation and Its Causes Seignorage and the Laffer Curve Dynamics of Seignorage Forced Saving International Exchange Rates Conclusions Exercises References and Suggested Readings 8. Government Finance in Stochastic Overlapping-Generations Models The Economy Some Examples A General Irrelevance Theorem Wallace's Modigliani-Miller Theorem for Open-Market Operations Chamley and Polemarchakis's Neutrality Theorem Interpretation as a Constant Fiscal Policy Indexed Government Bonds A Ricardian Proposition Further Irrelevance Theorems Conclusions Exercises References and Suggested Readings Appendix. Functional Analysis for Macroeconomics Metric Spaces and Operators First-Order Linear Difference Equations A Formula of Hansen and Sargent A Quadratic Optimization Problem in R A Discounted Quadratic Optimization Problem Predicting a Geometric Distributed Lead of a Stochastic Process Discounted Dynamic Programming A Search Problem Exercises References and Suggested Readings Index

564 citations

Journal ArticleDOI
Abstract: This paper develops a very general (general-equilibrium) intertemporal model of a country engaged in international trade which can be used to address a wide variety of issues of interest — in particular, econometric application — under the assumption that prices of tradable commodities (consumer goods and capital goods) and the interest rate are exogenous to the country. It allows for an arbitrarily large number of commodities which are distinguished into seven categories and for finite or infinite periods of time. This model can be used to draw various policy conclusions. We investigate how current net imports, the balance of payments on current account, current consumption expenditure, next-period bondholdings, current wealth, and current internal prices will react to exogenous changes in current external prices, the current interest rate, current taxes, current factor endowments, and current-period bondholdings. This paper also considers the integrability of net-import demand functions.

8 citations

Book ChapterDOI
Abstract: This paper considers explicit representations for very general (discrete and continuous-time) intertemporal consumption-maximization models which allow the instantaneous preferences of the consumer and the time-preference factors to vary over time and for the the non-existence of utility functions, more than one generation of consumers with a given probability of death, many commodities, and, further, a wide class of preferences which do not necessarily satisfy the so-called “regularity conditions” (such as differentiability, strict convexity, boundedness, or continuity) and include most of the well-known preferences in the literature.

2 citations

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Book ChapterDOI
Abstract: This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low prob- abilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. EXPECTED UTILITY THEORY has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice (24), and widely applied as a descriptive model of economic behavior, e.g. (15, 4). Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory (47, 36), and that most people actually do, most of the time. The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. In the light of these observations we argue that utility theory, as it is commonly interpreted and applied, is not an adequate descriptive model and we propose an alternative account of choice under risk. 2. CRITIQUE

34,961 citations

01 Jan 1944
Abstract: This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published "Theory of Games and Economic Behavior." In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.

19,323 citations

Journal ArticleDOI
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4,806 citations

Posted Content
Abstract: Ever since Richard Stone (1954) first estimated a system of demand equations derived explicitly from consumer theory, there has been a continuing search for alternative specifications and functional forms. Many models have been proposed, but perhaps the most important in current use, apart from the original linear expenditure system, are the Rotterdam model (see Henri Theil, 1965, 1976; Anton Barten) and the translog model (see Laurits Christensen, Dale Jorgenson, and Lawrence Lau; Jorgenson and Lau). Both of these models have been extensively estimated and have, in addition, been used to test the homogeneity and symmetry restrictions of demand theory. In this paper, we propose and estimate a new model which is of comparable generality to the Rotterdam and translog models but which has considerable advantages over both. Our model, which we call the Almost Ideal Demand System (AIDS), gives an arbitrary first-order approximation to any demand system; it satisfies the axioms of choice exactly; it aggregates perfectly over consumers without invoking parallel linear Engel curves; it has a functional form which is consistent with known household-budget data; it is simple to estimate, largely avoiding the need for non-linear estimation; and it can be used to test the restrictions of homogeneity and symmetry through linear restrictions on fixed parameters. Although many of these desirable properties are possessed by one or other of the Rotterdam or translog models, neither possesses all of them simultaneously. In Section I of the paper, we discuss the theoretical specification of the AIDS and justify the claims in the previous paragraph. In Section II, the model is estimated on postwar British data and we use our results to test the homogeneity and symmetry restrictions. Our results are consistent with earlier findings in that both sets of restrictions are decisively rejected. We also find that imposition of homogeneity generates positive serial correlation in the errors of those equations which reject the restrictions most strongly; this suggests that the now standard rejection of homogeneity in demand analysis may be due to insufficient attention to the dynamic aspects of consumer behavior. Finally, in Section III, we offer a summary and conclusions. We believe that the results of this paper suggest that the AIDS is to be recommended as a vehicle for testing, extending, and improving conventional demand analysis. This does not imply that the system, particularly in its simple static form, is to be regarded as a fully satisfactory explanation of consumers' behavior. Indeed, by proposing a demand system which is superior to its predecessors, we hope to be able to reveal more clearly the problems and potential solutions associated with the usual approach.

4,474 citations