The measurement of changes in real income under conditions of rationing in the United States during World War II
©2003
Diplomarbeit
58 Seiten
Zusammenfassung
Inhaltsangabe:Abtract:
During World War II, the private customers in the United States were confronted with conditions of rationing concerning several consumer goods. The government regulated the allocation of those goods, for example oil, leather, and grain, particularly with regard to their fitness to fight. The U.S. army was preferred to receive such goods instead of giving them to the citizens. Therefore, people had to optimize their consumption decisions with respect to both their budget constraint and rationing of goods.
Under the assumption that the households' preferences didn't change during World War II, one major trouble exists from the point of view of index number theory. Because of rationing, the prices of such goods usually change in contrast to a market economy, where the allocation of goods is presumed to be efficient, given prices which cannot be affected by the households consumption. Therefore the actual consumption of any given customer under conditions of quantity constraints need not be optimum with respect to his money outlay and the existing price system. In spite of rationing, the households optimize their utility from consumption given their money expenditures and the price system. Based on this relative strong assumption, one has to estimate a price system, which helps to measure changes in real income under such conditions of rationing. The central idea to solve that problem was introduced by Erwin Rothbarth (1941), who assumed that the quantities consumed under rationing were the same quantities consumed by households in an open market economy to receive their optimum. Rothbarth called such an estimated price system a _virtual price system_, which allowed him to work with the common index number theory. Such a virtual price system makes the quantities consumed under rationing a consumption optimum, i.e. the maximum level of utility, of the private customers. Rothbarth's method will be used in this article to estimate deflators, which will help to unlock changes in real income conditional on quantity constraints.
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 […]
During World War II, the private customers in the United States were confronted with conditions of rationing concerning several consumer goods. The government regulated the allocation of those goods, for example oil, leather, and grain, particularly with regard to their fitness to fight. The U.S. army was preferred to receive such goods instead of giving them to the citizens. Therefore, people had to optimize their consumption decisions with respect to both their budget constraint and rationing of goods.
Under the assumption that the households' preferences didn't change during World War II, one major trouble exists from the point of view of index number theory. Because of rationing, the prices of such goods usually change in contrast to a market economy, where the allocation of goods is presumed to be efficient, given prices which cannot be affected by the households consumption. Therefore the actual consumption of any given customer under conditions of quantity constraints need not be optimum with respect to his money outlay and the existing price system. In spite of rationing, the households optimize their utility from consumption given their money expenditures and the price system. Based on this relative strong assumption, one has to estimate a price system, which helps to measure changes in real income under such conditions of rationing. The central idea to solve that problem was introduced by Erwin Rothbarth (1941), who assumed that the quantities consumed under rationing were the same quantities consumed by households in an open market economy to receive their optimum. Rothbarth called such an estimated price system a _virtual price system_, which allowed him to work with the common index number theory. Such a virtual price system makes the quantities consumed under rationing a consumption optimum, i.e. the maximum level of utility, of the private customers. Rothbarth's method will be used in this article to estimate deflators, which will help to unlock changes in real income conditional on quantity constraints.
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 […]
Leseprobe
Inhaltsverzeichnis
ID 7221
Heilmann, Matthias: The measurement of changes in real income under conditions of
rationing in the United States during World War II
Hamburg: Diplomica GmbH, 2003
Zugl.: Freie Universität Berlin, Universität, Diplomarbeit, 2003
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Contents
1. Introduction
6
2. The data and some key facts and gures
8
2.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2. Key economic indicators of the U.S. economy . . . . . . 10
3. Estimating the households' demand system
15
3.1. Deriving the estimation equation . . . . . . . . . . . . . 15
3.2. The estimation of the households' preferences using the
method of ordinary least squares . . . . . . . . . . . . . 18
3.2.1. A general view on linear models . . . . . . . . . . 18
3.2.2. The OLS-estimation . . . . . . . . . . . . . . . . 20
4. Discrepancies in demand and exact deators
25
4.1. Dierences between actual and notional demand . . . . . 25
4.2. An outline of index number theory . . . . . . . . . . . . 26
4.3. Exact deators . . . . . . . . . . . . . . . . . . . . . . . 27
5. Conclusion
31
A. Personal Consumption Expenditures by type of expendi-
ture
34
B. Chained-type price indices
38
C. Disposable personal income
42
2
D. U.S. population
43
E. The categories of expenditure
44
F. Analysis of residuals
49
G. Observed and estimated demands
50
3
List of Tables
2.1. The 12 categories of expenditure . . . . . . . . . . . . . . 10
3.1. Estimated coecients (estimated standard errors in paran-
theses) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2. Estimated and observed budget shares (1945) . . . . . . 24
4.1.
Consumer Prices (P, 1996=100), Quantities (Q) and Expenditures
(X), observed and estimated values of 1945
. . . . . . . . . . . 29
4.2. Estimated Deators referred to 1946 . . . . . . . . . . . 30
4
List of Figures
2.1. Growth rate of annual per capita GDP, 1996 chained
Dollars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2. Growth rate of CPI, 1996 chained Dollars . . . . . . . . 12
2.3. Disposable personal income (1996 chained USD) . . . . . 13
2.4. Disposable personal income, annual growth rate . . . . . 13
2.5. Mid-year population (thousands) . . . . . . . . . . . . . 14
5
1. Introduction
During World War II, the private customers in the United States were
confronted with conditions of rationing concerning several consumer
goods. The government regulated the allocation of those goods, for
example oil, leather, and grain, particularly with regard to their tness
to ght. The U.S. army was preferred to receive such goods instead
of giving them to the citizens. Therefore, people had to optimize their
consumption decisions with respect to both their budget constraint and
rationing of goods.
Under the assumption that the households' preferences didn't change
during World War II, one major trouble exists from the point of view
of index number theory. Because of rationing, the prices of such goods
usually change in contrast to a market economy, where the allocation of
goods is presumed to be ecient, given prices which cannot be aected
by the households consumption. Therefore the actual consumption of
any given customer under conditions of quantity constraints need not
be optimum with respect to his money outlay and the existing price
system. In spite of rationing, the households optimize their utility
from consumption given their money expenditures and the price sys-
tem. Based on this relative strong assumption, one has to estimate a
price system, which helps to measure changes in real income under such
conditions of rationing. The central idea to solve that problem was in-
troduced by Erwin Rothbarth (1941), who assumed that the quantities
consumed under rationing were the same quantities consumed by house-
holds in an open market economy to receive their optimum. Rothbarth
called such an estimated price system a virtual price system, which
allowed him to work with the common index number theory. Such a
6
virtual price system makes the quantities consumed under rationing a
consumption optimum, i.e. the maximum level of utility, of the private
customers. Rothbarth's method will be used in this article to estimate
deators, which will help to unlock changes in real income conditional
on quantity constraints.
First, I will give an overview of the U.S. economy in chapter2. After
having done that, I will present several aspects concerning the calcula-
tion of a Rothbarian virtual price system. Thereby, it will be impor-
tant 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 house-
holds' 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 infor-
mation 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.
7
2. The data and some key
facts and gures
In this rst chapter some key economic facts based on the data I used
are presented. This might help the reader get a feeling for the economic
background in the last century in the United States of America.
2.1. Data
The data I use in this article are available at the Bureau of Economic
Analysis (BEA)-website (cf. [1]). The BEA delivers, among other
things, time series of dierent price indices, Gross Domestic Product
(GDP), and personal consumption expenditures. Of course not all of
the data is necessary in this article, therefore it follows a list of used
time series, which are annual data from 1929 to 2001:
1
Personal Consumption Expenditures by Type of Expenditure (cf.
[2], shortform cf. appendix A)
Chain-Type Quantity and Price indices for Personal Consump-
tion Expenditures by Type of Expenditure (cf. [3], shortform cf.
appendix B)
Selected Per Capita Product and Income Series in Current and
Chained Dollars (cf. [4], shortform cf. app. C and appendix D)
1
The delivered data sets contain the timeframe 1929 to 2001, but for most sub-
sequent estimations and calculations the timeframes 1940 to 2001 and 1946 to
2001 will be used.
8
All other relevant numbers are calculated by using entries in these
tables, especially the variables
Per Capita Personal Consumption Expenditures by Type of Ex-
penditure, and
Per Capita Real Expenditure (1996 prices).
The rst one is found by dividing the entries of tableA by those of table
D; the second series is calculated from the nominal values of table A
divided by 100, then multiplied by the entries of tableB to be divided
by table D to obtain per capita values. This calculation of per capita
variables is required, because both microeconomic demand theory and
index number theory assume single households and not an aggregated
point of view.
The data are ordered by N = 12 categories of consumption, which
are shown in table 2.1. Every single category is divided into several sub-
categories which are listed in appendix E for interested readers. The
households' consumption expenditures are assigned to these categories
to point out an as exact as possible view of the demand behavior of the
private sector.
9
Category No. Category name
1 Food and tobacco
2 Clothing, accessories, and jewelry
3 Personal care
4 Housing
5 Household operation
6 Medical care
7 Personal business
8 Transportation
9 Recreation
10 Education and research
11 Religious and welfare activities
12 Foreign travel
Table 2.1.: The 12 categories of expenditure
2.2. Key economic indicators of the U.S.
economy
We can extract some key indicators from the data to describe the de-
velopment of U.S. economy in the past decades. The most important
are shown in gures 2.1 to 2.4.
Figure 2.1 shows the annual growth rates of per capita Gross Do-
mestic Product (GDP) during the timeframe 1929 to 2001. Especially
in the middle of the 1930s until the beginning of Second World War in
1939, GDP grew with annual rates of about 10%. This must be seen
in respect to the 1929-Wall-Street-crash and the following worldwide
economic crisis (Great Depression), which determined a large world-
wide unemployment, crisis in the banking sector, high deation in most
industrial countries all over the world, etc. From that recession (with
annual shrinking rates of GDP of about 10% to 14%), the U.S. econ-
omy came back on track to prosperity pretty rapidly - till the Japanese
10
-0,2
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
0,2
19
29
19
34
19
39
19
44
19
49
19
54
19
59
19
64
19
69
19
74
19
79
19
84
19
89
19
94
19
99
Figure 2.1.: Growth rate of annual per capita GDP, 1996 chained Dol-
lars
attack at Pearl Harbor in 1941 and the resulting United States' ocial
entry into the war. Beginning in the late 1940s, we can identify sev-
eral peaks, and long-run limits of variation of about -3% and +7%.
The average long-run annual growth rate amounts to approximately
2%. In absolute terms the per capita GDP nearly quintupled starting
by approximately 6,700 USD in 1929 and grewing up to approximately
32,500 USD in 2001.
2
Another important economic indicator is illustrated in gure2.2: the
annual growth rate of the (aggregated) consumer price index (CPI), also
known as ination rate. The BEA publishes the chained-type price in-
dex
3
of personal consumption expenditures (cf. [3]), which has been
used to plot this gure.
2
Both numbers are valued at 1996 Dollars.
3
Besides price indices, quantity indices are also calculated. Chained-type indices
are calculated to show the development of prices of goods relative to the previous
period; another calculation method is using a xed period. Chained-type indices
are used by the U.S. and France for example, a representative of xed period
indices is Germany.
11
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
19
29
19
35
19
41
19
47
19
53
19
59
19
65
19
71
19
77
19
83
19
89
19
95
20
01
Figure 2.2.: Growth rate of CPI, 1996 chained Dollars
We can identify negative growth rates of the CPI especially in the
early 1930s. This deation of course is a result of the wordwide eco-
nomic crises mentioned above. During World War II high ination took
place with growth rates of up to 12% in 1942, followed by decreasing
rates until 1973, when the rst shock of a rising oil price let the prices
increase faster than in the decades before.
4
The long-run annual U.S.
ination rate averages about 3%.
The trend and the annual growth rate of disposable personal income
are presented in the following gures 2.3 and 2.4.
The disposable personal income rose in a nearly linear trend from
about 5,000 USD in 1930 up to 24,000 USD in 2001 (measured in 1996
chained dollars), which was conducted by annual growth rates in a
range between -15% and +14%. These extremely volatile growth rates
were observed especially in the rst half of the twentieth century. Be-
ginning in the 1950s, the annual growth rate stabilized at around 2%
4
The countries of the OPEC reduced their delivery of oil by approximately 25%.
12
0
5000
10000
15000
20000
25000
19
29
19
35
19
41
19
47
19
53
19
59
19
65
19
71
19
77
19
83
19
89
19
95
20
01
Figure 2.3.: Disposable personal income (1996 chained USD)
-0,2
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
19
29
19
35
19
41
19
47
19
53
19
59
19
65
19
71
19
77
19
83
19
89
19
95
20
01
Figure 2.4.: Disposable personal income, annual growth rate
13
Details
- Seiten
- Erscheinungsform
- Originalausgabe
- Erscheinungsjahr
- 2003
- ISBN (eBook)
- 9783832472214
- ISBN (Paperback)
- 9783838672212
- DOI
- 10.3239/9783832472214
- Dateigröße
- 787 KB
- Sprache
- Englisch
- Institution / Hochschule
- Freie Universität Berlin – Wirtschaftswissenschaften
- Erscheinungsdatum
- 2003 (September)
- Note
- 2,3
- Schlagworte
- schätzung deflator preismessung
- Produktsicherheit
- Diplom.de
