Munich Personal RePEc Archive
A Class of Dynamic Demand Systems
Tian, Guoqiang and Chipman, John S.
1989
Online at https://mpra.ub.uni-muenchen.de/41387/
MPRA Paper No. 41387, posted 17 Sep 2012 13:35 UTC
A Class of Dynamic Demand Systems
TL;DR: In this article, the authors derived closed-form solutions for the total consumption-expenditure 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.
Abstract: This 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.
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TL;DR: In this article, real dynamical macroeconomics models of real world macroeconomic models are presented. But the authors focus on real world economic models and do not consider the real world economy.
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
TL;DR: In this paper, a general-equilibrium intertemporal model of a country engaged in international trade is developed, which can be used to address a wide variety of issues of interest under the assumption that prices of tradable commodities (consumer goods and capital goods) and interest rate are exogenous to the country.
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
TL;DR: In this paper, 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 non-existence of utility functions, many commodities, and a wide class of preferences which do not necessarily satisfy the so-called "regularity conditions" (such as differentiability, strict convexity, boundedness, or continuity) were considered.
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
References
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TL;DR: In this article, the authors generalize the demand theory of Hicks and Allen for the dynamic case and derive income, price and interest elasticities of demand under the assumption that the individual has definite plans for the future and definite expectations of future incomes, prices, and interest rates.
Abstract: IT IS THE PURPOSE of this paper to generalize the demand theory of Hicks and Allen2 for the dynamic case. It also could give a somewhat firmer theoretical foundation to the dynamic demand theory of the Econometrists, especially G. C. Evans3 and C. F. Roos.4 We propose to derive income, price, and interest elasticities of demand under the assumption that the individual has definite plans for the future and definite expectations of future incomes, prices, and interest rates. Hence uncertainty in the sense of F. H. Knight5 is ruled out, whereas risk may be taken into account. We make the same assumptions as in the previous paper on "Maximization of Utility over Time."6 The individual plans for n discontinuous points in time in the discontinuous case, where utility is a mere function. Utility becomes a functional rather than a function in the continuous case.
25 citations
TL;DR: In this article, the existence of a utility function is assumed to depend on the quantity of goods the individual intends to consume at a given point in time, and the utility function will depend on those quantities which the individual expects to consume.
Abstract: SUPPOSE provisionally the existence of a utility function F. Let us assume further that the individual in question consumes only three goods x, y, and z. The argument can easily be extended later to any number of commodities. The individual is at the point in time 0 and plans for the period of time 1, 2, , n. Consumption takes place at these n discontinuous points in time. We denote by xi the quantity of the commodity x which the individual plans to consume at the point in time j; similarly, y2 and zj. He does not accumulate any commodity stocks. The utility function F will depend on those quantities which the individual expects to consume:
21 citations
TL;DR: In this paper, the identification and estimation of Lluch's extended linear expenditure system (ELES) from cross-sectional data alone is investigated, and all of the parameters of the ELES model are identified, and are estimable by the method of reduced form least squares.
Abstract: Complete sets of demand relations may be fitted using varying types of sample information and varying a priori specifications. In this paper the identification and estimation of Lluch's extended linear expenditure system (ELES) from cross-sectional data alone is investigated. Under the most favourable conditions of data availability, all of the parameters of the ELES model are identified, and are estimable by the method of reduced form least squares. This is the case where observations on permanent income are available for the consuming units of the cross section and where, in addition, prices are recorded (even though they do not vary from one consuming unit to the next). Under the least favourable conditions only the marginal budget shares are identified. This corresponds to the case where no data on permanent income, or on savings, are available. The conventional ordinary least squares estimators of the marginal budget shares are, under these conditions, biased and inconsistent. Expressions are developed for the large-sample biases.
16 citations
Book•
01 Jan 1977
11 citations