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• Publication Date: December 1, 1974
• Content Type: FORM

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SERIES NUMBER
A (ER) 74-64 (CRS seri
CLASSIFICATION OF REPORT
s) UNCLASSIFIED
DISTRIBWION TO RC
75,
DATE OF DOCUMENT
December 1974
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O
CIA I
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MEMORANDUM FOR: St/A/R
FROM: Chief, St/P/ C
Dissemination of A (ER) 74-64, Methods of
Constructing Economic Indexes From Income lete
Data (Project 00. 6944), Unclassified
You will receive 12 copies of subject report. It is requested
that they be disseminated as indicated below.
No. of Copies Recipient
~$ a St/SD
fl St/CS
]l D/C
D/U
2 D/I
1 D/S
I D/D
X5st]Mhxx
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23 January 1975
MEMORANDUM TO HOLDERS OF
RESEARCH AID A(ER) 74-64, Methods of Constructing
Economic Indexes from Incomplete Data, December
1974
1. The numbers appearing in Appendix B are outdated
estimates used solely for the purpose of testing the
procedures developed in this Research Aid. Please do not
use them for any substantive purpose.
2. A set of unclassified estimates of GNP and
industrial production will be disseminated in a few months.
Chief
Production Staff
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 Approved For Release 2000/05/11 : CIA-RDP79-00928A000100100001-3
Reference Aid
Methods of Constructing Economic Indexes
from Incomplete Data
A (ER) 74-64
December 1974
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.G. le
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This publication is prepared for the use of U.S. Government
officials. The format, coverage, and contents of the publi-
cation are designed to meet the specific requirements of
governmental users. All inquiries concerning this document
from non-U.S. Government users are to be addressed to:
Document Expediting (DOCEX) Project
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Washington, D.C. 20540
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 Approved For Release 2000/05/11 : CIA-RDP79-00928A000100100001-3
R
ES
A
Methods of Constructing Economic Indexes
from Incomplete Data
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 Approved For Release 2000/05/11 : CIA-RDP79-00928A000100100001-3
METHODS OF CONSTRUCTING ECONOMIC INDEXES
FROM INCOMPLETE DATA
1. In constructing indexes of an economy's performance, economists must
sometimes work with incomplete data. A typical problem involves estimating
missing values in a time series of industrial output, in order to compute an index
of industrial progress over time. In particular, the estimation problem presupposes
(1) an incomplete set of time series observations on quantities produced by
several industrial sectors and (2) a complete set of corresponding unit values
of output (for an illustrative set of data, see Table 1). The quantity produced by
the jth of n sectors in the tth of m years can be labeled Q(j, t), and the time-
constant unit value of the jth sector's output can be named P(j ). A time index
of total value produced by the n sectors is then
n
E (P(j) X Q(j, t) )
I(t) _ n X 100
E (P(j) X Q(j,b))
j=1
where b is the base year from which the index is computed. The problem is to
estimate the index I (t) for all years t=1, . . ., m, given that for each of these years
some but not all of the quantity observations Q (j, t) are missing.
Hypothetical Data on Industrial Output and Unit Values of Output
Industrial
Sector
Unit Value
of Output
1961
1962
1963
1964
1965
1966
1967
Ferrous metals
21
95
85
?
?
190
?
?
Fuels
17
118
177
236
295
354
324
?
Electric power
87
23
?
?
?
46
?
56
Chemicals
43
47
56
65
75
84
94
103
Lumber
24
83
103
124
145
166
186
207
Building materials
4
503
402
477
?
729
804
855
2. A procedure for this problem was suggested in 1960 by Kaplan and Moor-
steen.1 Two alternative and equally plausible procedures for the problem are the
Field method 2 and the naive method of linear interpolation, in which an analyst
merely uses a ruler to connect adjacent quantity values in a sector's time series of
output.
'Norman M. Kaplan and Richard H. Moorsteen, Indexes of Soviet Industrial Output,
Vol. I, RAND Corporation, Research Memorandum 2495, May 1960.
R.M. Field III, A Method of Constructing Index Numbers, unpublished memorandum,
CIA, Office of Economic Research, September 1974.
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 Approved For Release 2000/05/11 : CIA-RDP79-00928A000100100001-3
3. This publication
? explains each of the three methods, with reference to the sample data
in Table 1;
? presents computer programs for each method; and
? tabulates Monte Carlo tests of each method on five different sets of
Soviet economic data.
Principal Findings
4. In our tests of the three methods, the method of linear interpolation usually
produced the smallest errors in estimation. The Field method was second best,
and the Kaplan-Moorsteen (KM) placed third. This ranking resulted partly from
the fact that we based our tests on time series that usually grew smoothly. The
Field method would probably have excelled, had the series followed a cyclical
pattern. Further research might profitably be directed toward developing an es-
timation method better than any of the three considered in this report and toward
isolating classes of problems in which each method excels.
Kaplan-Moorsteen Method
5. Step 1. Calculate benchmark indexes B (t) for years in which output data
are available for each industrial sector. If the data are not complete for at least
two years, the method does not apply. Since the sample data in Table 1 are com-
plete for the first and fifth years (1961 and 1965), the benchmark indexes are
6
>; (p(j) X Q(1, 1) )
j=1
6
(I'(j) X Q(j, 1) )
j=1
6
>2 (P(j) X Q(j, 5) )
r,~, j=1
6
>2 (P(j) X Q(j, 1) )
j=1
where we have selected year 1 as the base year.
6. Step 2. Calculate average annual rates of growth between each successive
pair of benchmark indexes. Since the sample problem contains only two bench-
mark years (1 and 5) we calculate a single growth rate (M>X)/0
161 DR4-?M
171 Dc'.-?N
181 YDIDR;DC]1,1
Subroutine to Compute the Actual Indexes
V ACTIND[ ^IV
V ACTIND;AIN;IZ
III M COMPUTE ACTUAL INDEXES
[21 A]-?O
131 AIN