[...] First, I will give an overview of the U.S. economy in chapter 2. After
having done that, I will present several aspects concerning the calculation
of a Rothbarian virtual price system. Thereby, it will be important
to build an opinion about the preferences of the private households,
which will be expressed as a generalized Cobb-Douglas demand system.
Based upon that demand system an estimation equation for the households'
preferences will be derived in section 3, followed by an ordinary
least squares regression of the preference parameters.
The second important step will be a presentation of the basic information
we can win from index number theory. It will be especially
interesting to say a few words about economic index number theory
(see chapter 4.2).
The combination of the outcomes from estimation with index number
theory makes up the most important step to unlock hidden dierences
between wartime-prices and postwar prices, i.e. I will compare wartime
demand to postwar demand and the impact of rationing on changes
in income. This procedure will be done by calculating deators using
both the estimated demand behavior and virtual prices.
In every section, I will present both the basic theoretical aspects,
which will help the reader understand the steps to deators, and applied
theory, i.e. estimations using empirical data in most cases.
Table of Contents
1. Introduction
2. The data and some key facts and figures
2.1. Data
2.2. Key economic indicators of the U.S. economy
3. Estimating the households' demand system
3.1. Deriving the estimation equation
3.2. The estimation of the households' preferences using the method of ordinary least squares
3.2.1. A general view on linear models
3.2.2. The OLS-estimation
4. Discrepancies in demand and exact deflators
4.1. Differences between actual and notional demand
4.2. An outline of index number theory
4.3. Exact deflators
5. Conclusion
A. Personal Consumption Expenditures by type of expenditure
B. Chained-type price indices
C. Disposable personal income
D. U.S. population
E. The categories of expenditure
F. Analysis of residuals
G. Observed and estimated demands
Objectives and Topics
This work aims to measure changes in real income for U.S. households under rationing conditions during World War II by employing Rothbarth's concept of a "virtual price system." The central research question focuses on how households optimized consumption decisions under simultaneous budget constraints and wartime goods rationing.
- Analysis of U.S. economic data and indicators during the 20th century.
- Specification and estimation of a Cobb-Douglas demand system.
- Application of ordinary least squares (OLS) regression to estimate household preference parameters.
- Utilization of index number theory to derive exact deflators.
- Comparative analysis of observed versus notional demand to identify the impacts of rationing.
Excerpt from the Book
3.1. Deriving the estimation equation
A formal specification of a Cobb-Douglas demand system is as follows. In a market economy, the utility that a household can achieve is usually written as
U = Π_{i=1}^{N} q_i^{a_i}, 0 < a_i < 1 (3.1)
The utility is expressed as the product of consumed quantities, weighted by preference parameters a_i. Maximizing this utility subject to the households' budget constraint y >= Σ_i p_i q_i leads to Marshallian demand functions q_i(p, y). If we replace these demands in the Cobb-Douglas utility function (3.1), the resulting expression is called "indirect utility", which depends on a vector of prices of goods p^t and the household's budget constraint y^t at any point of time, t = 1, . . . , T. From the available data, the series "Disposable personal income (1996 chained Dollars)" is equivalent to the (exogenous) budget constraint.
Then the indirect utility function can be written in a formal general expression:
ν_t(p^t, y^t) = Π_{n=1}^{N} (y^t / p_n^t)^{β_n^t} (3.2)
The quotient y^t / p_n^t represents the quantities q_i^t of goods and services consumed in any period as mentioned in equation (3.1). In empirical works, researchers are often confronted with the problem that those quantities cannot be observed directly, but there are many income series and price data measured, so that these are used to calculate implicit quantities. The budget shares β_n^t for all n = 1, . . . , 12 categories of expenditure must of course sum to unity in any period t, that is Σ_{n=1}^{12} β_n^t = 1. Using this and the exogenous disposable income, the indirect utility function (3.2) should be transformed into
ν_t(p^t, y^t) = Π_{n=1}^{N} y^t / (p_n^t)^{β_n^t} (3.3)
Summary of Chapters
1. Introduction: The introduction outlines the context of wartime rationing in the U.S. and introduces the central method of using "virtual prices" to measure real income changes.
2. The data and some key facts and figures: This chapter presents the economic datasets and key macroeconomic indicators for the United States from 1929 to 2001.
3. Estimating the households' demand system: This chapter defines the theoretical framework of the Cobb-Douglas demand system and applies OLS regression to estimate preference parameters.
4. Discrepancies in demand and exact deflators: This chapter compares actual and notional demand patterns and utilizes index number theory to construct exact deflators for the rationing period.
5. Conclusion: The conclusion synthesizes the findings regarding the economic impacts of rationing, specifically substitution effects and real income development.
Keywords
World War II, Rationing, Real Income, Virtual Price System, Cobb-Douglas Demand System, Household Preferences, Ordinary Least Squares, Index Number Theory, Exact Deflators, Disposable Personal Income, Consumption Expenditures, Economic Indicators, Substitution Effects.
Frequently Asked Questions
What is the primary subject of this research?
The work examines the measurement of changes in real income for American households during World War II under conditions of severe goods rationing.
What are the main thematic areas?
The main themes include household demand systems, empirical econometrics, index number theory, and the economic analysis of wartime rationing impacts.
What is the core objective of the study?
The objective is to calculate the hidden impact of quantity constraints on real income by applying Rothbarth's virtual price system method.
Which methodology is employed in the analysis?
The study uses a formal Cobb-Douglas demand system, estimated via ordinary least squares (OLS) regression, combined with index number theory to derive exact deflators.
What does the main body cover?
The main body covers data sourcing, the derivation of the demand estimation equation, the technical OLS-estimation procedure, and a detailed analysis of discrepancies between observed and notional demand.
Which keywords characterize this paper?
Key terms include rationing, virtual prices, demand system, Cobb-Douglas, real income, and OLS-estimation.
How does the author handle non-observable wartime quantities?
The author uses implicit quantities derived from disposable personal income series and price data to overcome the lack of direct quantity observations during the war.
What is the purpose of the virtual price system?
It allows the researcher to treat consumption under rationing as if it were an optimal choice in an unconstrained market, thus enabling the use of standard index number theory.
- Quote paper
- Matthias Heilmann (Author), 2003, The measurement of changes in real income under conditions of rationing in the United States during World War II, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/17272
