A METHOD FOR STATISTICALLY
DETERMINING INFLATION –
CALCULATING THE “GENERAL INDEX
OF INFLATION” (IGI)
Vasile V. DUMITRESCU, PhD.
Gheorghe SĂVOIU, PhD.
Abstract
We can do the actual quantifying of inflation by exploiting a general index
(IGI) by performed using an aggregate Laspeyres index that capitalizes on a set of
six specific indices, out of which the general index of consumer prices (CPI) should
hold an important but not also unique place, transforming this statistical construct
into an interpret index whose area is much broader, being also based on aggregation
coefficients previously determined in a rigorous manner. This is the theme, and hence
the solution the present paper offers in order to measure inflation in an exhaustive
statistical manner, in point of coverage and starting from the gross income of the
population (VBTP). The alternative defines a joint project of the authors, described
theoretically in another paper published in this journal (RRS, Supplement no. 10/2016)
addressing the need for a general inflation index (IGI).
Keywords: aggregate index, interpret index, consumer price index (CPI),
general index of inflation (IGI), Laspeyres-type index, weights, weighting system,
weighting coefficients.
1. Introduction
In researches addressing the contemporary market economy, a topic that
requires special attention is represented by inflation, which has major cognitive and
delimitative purposes within regional cyclical contexts of evolution. This type of
inquiry, which, initially, was dominantly theoretical, and then set in a significantly
pragmatic perspective, offers a wide range of issues concerning: a) a clear and
complete definition of the concept; b) detecting the multiple causes that trigger the
phenomenon; c) studying and analyzing the economic policies applied in the macroeconomic system investigated; d) the external influences and other disruptive factors
of inflation; e) the manner of establishing the evolution, variation, quantifying or
measuring inflation; f) developing measures and solutions to mitigate and combat
surging trends, etc. As part of such research, an important role is played by the manner
of statistically determining inflation, which is in fact the very basis of the entire
investigation: Correct quantification of an aggregate index of inflation requires an
exhaustive analysis of improvement, and also of improvement, as well as generating
new calculation methodology solutions for indicators expressing, comprehensively
and as realistically as possible, the level and trend of inflation at a certain point in
time, and also the application of methods and techniques of drafting nomenclatures,
selection, observation, collecting, transmission, processing and dissemination of
statistical data and information to multiple recipients, from the public at large, to the
public institutions and economic entities concerned..
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2. A specific procedure for calculating the Inflation General Index (IGI)
Research aimed at determining the level of inflation is based on the thinking
specific to the method of statistical indices, and statistical science in general, which requires
a systemic and comprehensive approach, or exhaustive knowledge of all, or nearly all,
issues, terms and elements that are being operated with, in the design and construction
of indicators in economics. Never can the difficulty of statistical thinking be omitted, as
Professor Daniel Kahneman, the 2002 economics Nobel Prize laureate, demonstrated: “…
why is it so difficult for us to think statistically? It is easy for us to think in an associative,
metaphoric or causal manner, but statistics requires us to think about several things at
once…” (Kahneman 2012, p. 30), a systemic or complex approach that allows one to
obtain realistic results, resisting both the temptations of retrospective and the illusions of
uncertainty, without however exaggeration confidence in what is already known, in what
is achieved, what is being dealt with, or what is already being quantified statistically. In
other words, in economics there are always resources for a better statistical evaluation as
long as one does not underestimate the opportunity of thinking and innovating methods,
models and tools that are considered sufficiently accurate…
The process of determining inflation statistically aims to establish the effect of
current prices and tariffs, which lead to diminished buying power of a national currency.
It would be natural to think of purchasing power, in somewhat broader terms, as of the
payment power of the national currency, or more accurately, the payment power of all
types of incomes in a national economy. For example, in order to achieve that coherently
and systemically, in the spirit of statistical thinking, ther a major element missing here,
which may be referred to simply as share (or possibly quota) of revenues, becoming, more
concretely, deducting from the gross income, in the already economically standardized
form of taxes, contribution to social insurance, health insurance, unemployment
contribution, etc., and which pertain or accompany all the sums of money defined as
the gross income of the population. Such an improved approach could lend a clearer
delineation of the payment capacity of the national currency, thus contributing to a more
accurate expression of the quantification of inflation, through a new index synthetically
expressed by the General Index of Inflation (IGI).
The need to reshape or rebuild a tool for calculating inflation, as the General
Index (or Indicator) of Inflation (IGI) is triggered by the over-evaluating or excessive
approach of the present, in which it is considered that inflation is expressed accurately
by under-evaluating instrumental innovation by the Consumer (goods) Price Index
(CPI), and as such the gross / net incomes of the population, i.e. salaries, pensions,
unemployment benefits, etc., can be determined very clearly, and especially in real
terms.
The reader or consumer can correctly find that the two indicators alone can
not be and are not comparable in terms of content, structure and scope.
Inflation is a complex process of overall increase in prices, tariffs and quotas,
a process that sometimes takes place faster, and sometimes more slowly, possibly even
in a galloping or hypertrophied manner, and maybe even in the opposite direction,
when it turns to deflation, which is currently called, more and more frequently,
negative inflation, in keeping with the after-effect of the increase in prices of consumer
goods and durables, the pricing of services used by population, and also of the quotas
applied, which, over time, erode or diminish the purchasing power of a number of net
incomes, and also the paying power of the domestic currency, with a severe and direct
impact, to a similar extent, on the gross income of the population.
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Components of determining inflation combine the currency, as a means of
purchase (IPC) or a means of payment (IGI), net incomes (IPC), but especially net
incomes (IGI), as well as prices and tariffs (CPI), generically also including quotas
(IGI) and other decreases in gross revenues for the population, which the latter take,
in a manner that is more or less independent of their will.
Scientifically establishing the balance and direct correlation between the
content, the structure and the scope of the decrease in purchasing power or payment
power of the national currency, of the gross income of the population, and the growth of
prices, tariffs and quotas applied, requires a good knowledge of the elements underlying
the statistical indicators expressing contemporary inflation in a broader sense:
a) currency is a means of purchase or payment, a means of exchange,
accumulation, savings and increasing wealth (getting better-off), of evaluation and
value expression of goods and services, by means of statistical indicators of values
or financial indicators (expressing an ineluctable economic character), a means that
cannot have a constant value, or a value eternally placed at the same level in a multicurrency system, and which usually loses its power of payment or purchase over time
(which resulted, during its history, in the need to denominate, or even reform it, with
the stated purpose of strengthening it, in the desire to make it stronger on both the
domestic and foreign market – a result that was achieved by resorting to statistical
methods, procedures and techniques that provide data and information on determining
the level of decline, and enabling the development of corrective measures which
needed be taken historically);
b) the gross incomes of the population comprise all money amounts due,
that are received in cash, in a more and more varied form, ranging from salaries
to pensions, allowances, bonuses, premiums, including deductions in taxes, social
security contributions, health insurance, unemployment, which are deductible from
those amounts, as well as welfare or unemployment benefits, allocations, dividends,
interest, bonuses, life percentages, the value of Easter or Christmas gift vouchers,
the value of different types of vouchers and dinner vouchers, proceeds from the
sale of property, rental, gambling, lottery, betting, revenue raised as bank loans for
consumption and/or investment for housing or other assets, amounts received from
certain people in the country or abroad, and other income received in any form.
c) the prices, tariffs and quotas or rates charged and paid by the consumers, users
and end payers trigger the process, and ultimately determine the level of inflation,
affecting the purchasing power or payment power of the respective currency, or
the gross income of the population, as they are influenced in turn by thr universe
of the categories of prices, tariffs and quotas that are applied in the system of the
complex relations of exchange, payment, of interference and interconnection,
which are created and form during the flow of accessing energy, raw materials –
the production and / or supply of services – intermediate consumption, selling or
actual supplying by the transfer of ownership – final consumption, including exportimport flows, which are multiple and varied, fluctuating over time, and different in
level both between entities of the same profile, and sector-wise, territorially, and
also according to the types of activity, in keeping with the practices and economic
policies applied as pat of the specific hyper-system of a national economy. The
prices and tariffs for the goods and services purchased or used by economic entities
/ legal entities are included in their cost of production, and are later covered by the
aggregate prices and tariffs of goods manufactured and services rendered.
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Among the three components described above there is a certain, direct and
intense qualitative association, which is much more easily found in conditions of
a relative stability of gross income, or currency (its purchasing power, or payment
power), which puts pressure on the prices, tariffs and quotas applied to final payments;
this describes, concretely and specifically, an “effect of balance”, and any increase
in revenues should be based on performance or productivity growth, in the overall
context of the general development of the country’s economy, which is likely to lead to
the strengthening of the national currency and a redistribution of population welfare:
any unjustified or unsustainable increase can conduce to an automatic increase in
inflation, a decrease in the purchasing power of the currency, and implicitly a decrease
in the gross income of the population.
The impact of price and tariff increase – similarly and cumulatively descending
– comparatively and simultaneously as to the increase in quotas
Figure 1
Source: Developed by the authors with respect to the upward trend of wages, tariffs
and quotas
The creation and organization of statistical databases are indispensable
prerequisites of the construction of an interpret index, or an index that assesses the
developments in time of prices, tariffs and quotas, i.e. of general inflation.
Determining inflation is based on developing the existing statistical
information system, in order to ensure the needed, complete amount, in an orderly,
structured and detailed manner, at the required level of data and information, in
accordance with such principles and criteria that are clearly set out in instructions and
rules allowing the collection and recording, in an organized, operative and accurate
way, of both pricing and tariffs, as well as quotas.
The information system should be integrated so as to provide data and
analysis components useful in characterizing the welfare of the population, as well
as real, actual data needed for constructing the indices concerning the evolution and
change or variation in consumer prices, prices of durable goods, tariffs for the services
targeted at, and provided for the population for personal needs, as well as the quotas
practiced.
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The statistical data and information regarding the construction of indicators expressing
general inflation (IGI), require a more detailed presentation compared to the solutions
presented above, which can be described as follows:
I. The total gross revenues of the population, structured and aggregated in
keeping with the spending destinations depending on the content, the structure of the
component elements, their nature and homogeneity, targeted at purchasing consumer
goods, services for personal use, binding payments (quotas), investment, buying
currency and stock exchange shares, which enable us to determine the weighting
coefficients of prices, tariffs and, of course, quotas, etc.
The total household gross income, broken down by destinations, can be
obtained through surveys of the “budget of family income and expenditure” (ABF,
formerly AIG), which include revenues from the period of observation and reporting,
as presented above, deconstructed or disaggregated in keeping with:
a) the way they are obtained: i) gross salaries, including bonuses, allowances,
bonuses etc., obtained from carrying out various activities; ii) gross pension; iii) social
welfare; iv) other types of income.
b) the method of payment: i) cash; ii) other means of payment.
c) their final destination: i) for the expenses; ii) intended for the payment of
(binding) quotas; iii) for investment; iv) for the purchase of foreign currency; v) for
purchase of shares; vi) savings.
By aggregating these revenues, in keeping with their final destination, they
are conducive to the determination of distinctive weightign coefficients necessary for
the construction of a set of indices.
The revenues for expenses generate, through aggregation, the weighting
coefficient accompanying the ‘Consumer (goods) Price Index’ (CPI), and are
characterized by purchasing consumer goods and using services for personal needs,
basic necessities, deconstructed by categories of food products, non-food goods, and
services. The content and structure of the goods and services purchased or used by
the public represents the basis for determining the “monthly basket of expenses”, of
the the nomenclature used to construct the CPI, which, through detailing by groups,
expenditure positions, and items with a share of consumption or use, become defining,
and subsequently allow statistical research meant to establish the representative
assortments/varieties, in particular regarding garments, knitwear, footwear, medicines,
electrical appliances, health services and tourism, transport and communication, etc.
The revenues for mandatory/binding payments (quotas) by individuals, to
state institutions or private entities generate, through aggregation, the weighting
coefficient that accompanies the “Index of variation of the incomes for payment of the
public’s binding quotas (allowances) (IVVDPOP)”, which requires a new research
approach regarding their introducing in the statistical information system, which has
a significant influence on the level of inflation, on account of its volume, content,
diversity and specificity, being homogeneous its in nature and unique character; they
also are binding through the fact that revenues, and expenses, respectively, must be
detailed differently by categories of quotas, depending on how they are practiced: in
percentage (%), such as direct taxes, contributions, interest on bank loans; or value
rates such as the fees are based on certain criteria for establishing their level, for
example: determining the value of insurance policies in case of automotive civil
liability (RCA), which takes account of the engine capacity and age of the insured
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person; or there are nominal value rates set arbitrarily depending on budget needs, tax
needs, or specific local conditions.
Revenues for investments made by individuals, including bank loans taken
for this purpose, generate, by aggregation, the weighting coefficient accompanying the
‘Price Index Investment (IPI)’, and should be structured according to the composition
of the purchases made in connection with dwellings, other buildings, land, cars and
appliances, animals, valuables and other goods. This index requires a new approach
concerning its scope, and introducing in the system the assessment and calculation
elements for the components that produce price changes.
Revenues for the purchase of foreign exchange by individuals, both for
repayments on bank loans, and for payment of travel packages or other services that
represent personal needs, generate, through aggregation, the weighting coefficient that
accompanies the “Exchange Index” (ICV). Detailing and aggregation of these revenues
must result in statistical practice, as it is an increasingly active area, which can provide
data and information regarding the expression of variation and average evolution of the
national currency against the euro (or dollar, or other currencies on the market); currency is
bought, and respectively sold by banks or firms specializing in the activity of the foreignexchange, during the reference calculation period (month, quarter, semester, year).
Revenues for purchase by individuals of shares in the stock market or
from the Stock Exchange constitute a specific form of investing money or saving it,
which changes over time and generates, by aggregation, the weighting coefficient
that accompanies the “Index of Stock Exchange Quotations” (ICB). This index is
specific to the stock market, and has a certain scope which concretely expresses
the developments in stock prices for a certain category of units listed on the Stock
Exchange. ICB represents a component of inflation, which makes it urgently requisite
to introduced in the statistical information system the tracking of these quotations,
which add precision and realism in determining the level of generalized increase in
prices, tariffs and quotas, but equally the decrease in the purchasing power of the
gross income of the population or of the national currency.
The Exchange Index (ICV) and the Index of Stock Exchange Quotations (ICB)
have a particular specificity, and through their content, they include expenditures by
individuals. Determining ICV and ICB can capitalize especially on average weighted
quotations, at the level of nominal position of the changes with an inflationary effect.
The revenues that, by their nature, were not part of any of the five destinations,
such as, for example, the savings in bank deposits, in government securities, optional
insurance policies, or mere household saving schemes, can be considered a form of
saving that has no inflationary effect, but which may be affected by inflation (in which
case an index can be chosen to accompany them, which is strictly stationary, IS =
100%, or an index of the purchasing power of the domestic currency in the previous
month – IPCMN in month t-1), and through aggregation, it generates a weighting
index accompanying the final index actually opted for (IS = 100%, or IPCMN in
month t-1).
II. The final prices and, as well as the quotas borne by the consumers, end
users and payers, which underlie the construing of the specific partial interpret indices,
pertaining to the General Index of Inflation (IGI), can be obtained by extending and
adapting the current statistical information system for obtaining the respective data, by
conducting the developing of detailed nomenclature lists up to the elementary level of
Revista Română de Statistică - Supliment nr. 11 / 2016
17
assortment, variety, price, tariff, nominal quota, which must be representative and/or
characteristic, being based on standards, rules and clear instructions for observation,
collecting, conveyance and processing, in the following fields: finance, budgetary,
fiscal matters, banking, insurance, investments, exchange rates, stock exchange
quotes, as well as for developing methodologies for building the respective indices
that express inflation.
III. The general index of inflation (IGI) thus constructed expresses the
effect of reducing the purchasing power of the population or the payment power of the
national currency, namely the payment power of the total household gross income. IGI
includes the calculation of five specific partial interpret indicators, established by the
nature of their components, having a homogeneous and unified content, determined
by applying the weighting coefficients of the revenues for actual costs, at the prices,
tariffs and quotas applied in the national economic system, which ultimately express
the evolution, variation and level of inflation.
The systemic approach to determining inflation and quantifying the level
of decrease in the purchasing power of total income of the population, or decrease
in the payment power of the national currency, lies in that the scope is broadened
of the component elements that are taken into consideration, taking into account the
effect that all prices, tariffs, quotas and quotations practiced have, which are paid, i.e.
borne by individuals from their own income for consumer goods or durables, for using
service and payment of mandatory payments (quotas), purchase of foreign currency
and shares, obtained in the final stage.
To achieve those requirements in the best conditions, it is necessary there to
be a close cooperation between the specialists in the field of statistics of the quality
of life or the welfare, and those in the field of the statistical methodology intended
to build indices, in order to establish a correlation with full coverage between the
content and the structure of the chapter concerning the total gross household
income and the nomenclatures underlying the observation of the prices, tariffs and
mandatory payments (quotas), observed (collected and recorded) for the construction
of the indexes mentioned. Also, a very important role is played by the statisticians
and interviewers in Family Budgets surveys (ABF), who must carefully watch the
way of filling in the sheets, permanently, in the households included in the sample,
monitoring the accuracy and timeliness (i.e. on a daily basis) of the records in order to
obtain statistical the true and complete data and information necessary.
The general index of inflation (IGI) is a statistical indicator of topmost economic
synthesis economic, which expresses the level of the decrease in the purchasing power
of the total gross income, or the level of decrease in the payment power of the national
currency, being rendered by an equal decrease of the total gross revenue of the population
affected by rising prices, tariffs and quotas borne by the consumer, the end user and the
end payer. The complexity of this index requires the construction aided by a formula of
a polynominal type, which is based on a broad scope of coverage of the effect of the
five specific and partial interpret indices, plus, in the first month, a sixth index, which is
stationary (IS = 100%), later replaced by an index shifted to time t-1 of the purchasing
power of the domestic currency (IPCMN): the construction, thus aggregated, expresses
much more clearly the overall level of inflation.
Essentially, we start from a Laspeyres-type formula (to ensure the unitary
principle of statistical quantifying, as CPI is currently determined as a Laspeyrestype
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Romanian Statistical Review - Supplement nr. 11 / 2016
index, as well, but also for practical reasons related to the lag required to achieve and
verify the calculations), by making use of a usual artifice of calculation:
n
n
¦p
q0i
¦p
q0i
1i
1i
q0i u
i 1
i 1
n
IGI
¦p
n
0i
i 1
¦p
i 1
p0 i
p0 i
n
¦p
0i
q0i u
i 1
n
0i
q0i
¦p
i 1
p1i
p0 i
n
¦( p
0i
q0i ) u i1p/ 0
i 1
n
0i
q0i
¦p
0i
q0i
(1)
i 1
where, if the weighting coefficient of the income groups is noted by W, as determined
by the relationship:
( p0i q0i )
W=
n
¦p
0i
q0i
(2)
i 1
then the formula of the index of a polynominal type (IGI) comes as the
average of the general collectivity, where the last term is quantified, for the first year
alone, as IS=100%, i.e. different from IPCMNt-1
n
IGI =
¦W
0i
u Ispecific
i 1
(3)
or, specifically, by appealing to the five specific indexes, it becomes:
IGI = W0IPC×IPC+W0IVVDPOP×IVVDPOP+W0IPI×IPI+W0ICV×ICV+W0ICB×ICB+W×IPC
MNt-1
(4)
where: in the first year of calculation IPCMN = IS = 100%, and in the other
years IPCMNt-1 = IGI t-1
The general index of inflation, consisting of the specific partial interpret
indexes, is calculated, practically, in two steps:
a) in the first stage, the five specific partial interpret indexes are constructed,
where:
W0i = the weighting coefficients in the base (previous) period, established
in keeping with the structure of the five specific partial interpret-type indices of the
incomes, i.e. of the expenses incurred in the base or previous comparison period,
detailed up to the level of elementary indices,
I1/0i = the individual/elementary indexes for pricing, tariffs, mandatory
payments (quotas), specific at the level of assortments/varieties, as part of the five
speicific interpreter indices;
IP, IVVDPOP, IPI, ICV și ICB = specific partial interpret indices for the five
destinations;
b) In the second step the weighting coefficients of the specific partial
interpret indices are construed, based on the share or weight of the total gross revenues
allocated, assigned for the five indices:
The sum of the W0i coefficients of the six partial specific interpret indices
established based on the destinations of the total gross revenue, i.e. the expenditure, is
equal to 1:
WIPC + WIVVDPOP + WIPI+ WICV+ WICB+WIPCMNt-1 = 1
(5)
Revista Română de Statistică - Supliment nr. 11 / 2016
19
Finally, by weighting the partial specific interpret indices with the weighting
coefficients (W0i) established for the six destinations, we obtain the General Inflation
Index (IGI). The sum of the successive aggregations of the specific interpret indices
for pricing, tariffs and obligatory payments (quotas) is the general index of inflation
(IGI), a statistical construct adapted to the reality of today’s market economy, and
it provides full coverage of the gross income of the population, which instrumental
renders the quality of real expression of the level of inflation, and corresponds to the
decrease in the purchasing power of the total gross income, or the payment power of
the national currency recorded during the calculation period. It can be estimated that
the general index of inflation (IGI) has a coverage of over 80% of the Gross Domestic
Product (GDP), calculated using the method of final consumption or final expenditure,
but it fails to reflect the trends in prices and tariffs for buying goods, using services, by
public State institutions or legal persons for gross capital formation and the prices of
exported goods, in the event of a surplus trade balance.
3. Conclusions
The systemic approach to inflation research, based on statistical thinking,
allows inclusion within one indicator of the evolution of the main categories of prices,
taxes and mandatory payments (quotas) borne by individuals, as consumers, users and
tax-payers, in the final phase, which offers those interested in this issue the opportunity
to fully analyze the total influence, and the innfluence in each component, in the actual
change (actual increase or decrease) of gross income, namely the increase or decrease
in the purchasing power of their total gross income, or in the variation of the payment
power of the national currency. The authors plan to complete the project of this new
statistical construction in a future paper, by actually quantifying a General Index of
Inflation (IGI) in the Romanian economy, which is to be submitted to a statistical
confrontation with the current construction of the Consumer Prices Index (CPI), thus
revealing its greatly improved concrete valences and practical use.
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