# Measurement by liaoqinmei

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```									1     Measurement
As explained in the previous chapter, measurement is a key component of the scientiﬁc
method and is necessary to develop and validate theories. Sherlock Holmes, one of the
masters of (investigative rather than economic) theory, once said:

"Data, data, data: how can I make bricks without clay?".

Without measurements, macroeconomics could not be a social science, and would
be more similar to philosophy.
Market transactions provide the most simple and direct measurements: through
market transactions we can observe both quantities and prices.

1.1     Measurement of GDP
In the United States, the oﬃcial source of measurement of aggregate GDP and its
components is the National Income and Product Accounts (NIPA) collected by
Bureau of Economic Analysis, an agency of the U.S. Department of Commerce.
Nominal GDP Yt is the dollar value of all ﬁnal goods and services produced within
the borders of the US in period t. There are three approaches to measurement of GDP:

1. the product (value added) approach,

2. the expenditure approach,

3. the income approach.

According to this method, nominal GDP, which we will denote as Yt , is calculated
as the sum of the value added (V A) to intermediate goods and services by all the
production units (public and private ﬁrms) in the economy. The value added V A (i)
for a given good i is obtained from the value of all sales of good i in the economy,
subtracting the costs associated to the purchase of all intermediate goods needed to
produce the sales of i.

V A = value of sales - purchase of intermediate goods

Hence, we obtain
X
I
Yt =         V A (i)
i=1

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One important question arises: why do we sum only value added and not all sales? To
avoid double counting. The value added is the correct measure of the contribution
to production of a ﬁrm

• Example: 3 ﬁrms, A produces \$100 of steel and sells to ﬁrm B, say Ford,
which uses the steel to produce \$300 of cars. Firm B sells to C which is a car
dealer, parks the cars in ht eparking lot and sells them for \$400. Total output is
\$100+\$(300-100)+\$(400-300)=\$400. Put it diﬀerently, only \$400 of cars sold by
C to households are a ﬁnal good.

EXPENDITURE APPROACH
With this method, GDP is calculated as total spending on all ﬁnal goods and
services produced in the economy. We need to use the fundamental equation of National
accounting that states that aggregate income equals aggregate expenditures, or

Yt = Ct + It + Gt + (Et − Mt ),                          (1)

where the component of the expenditure side are:

• Consumption C includes durable goods (car, TV, PC, IPod), nondurable goods
(food, drinks, clothing), services (nontangible items like education, health, hair-
cuts, consulting, entertainment). A big component of services is housing. For
renters, houseing expenditures are just the value of rent paid. What about for
homeowners? NIPA imputes a value of rent expenditures for homeowners by
looking at how much tenants of similar houses (same size, neighborhood, etc...)
pay in rent.

• Gross investment I is the sum of non-residential ﬁxed investments –expenditures
of ﬁrms on equipment (industrial machines, cars, PC’s) and structures (plants)–
plus residential ﬁxed investment (new houses), plus the change in their invento-
ries.

— Net Investment (gross investments minus depreciation) ItNET represent
the addition to the capital stock of the nation

Kt+1 = Kt + It − DEP Rt                           (2)
= Kt + ItNET ,

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where ItN ET is the ﬂow of net investments. Hence the capital stock is the
quantity of housing, plants, equipment, and inventories existing in the econ-
omy at a given point in time. It is useful to develop equation (2) recursively,
to show that the capital stock of a nation is the historical sum from today
to its far past of all the (undepreciated) investments made, i.e.

Kt = It−1 − DEP Rt−1 + Kt−1 = It−1 − DEP Rt−1 + It−2 − DEP Rt−2 + Kt−2 = ...
X∞
=     (It−j − DEP Rt−j )
j=1

Remark 1 Note that capital is a stock, i.e. it is measured at a point in
time, whereas investments (and all other expenditures) are a ﬂow, i.e. their
measurement refers to a period. Investment in 2003 means all the expendi-
tures in investment goods from 1/1/2003 to 12/31/2003.

• Government spending G is the sum of all purchases of goods (e.g., pencils
for employees) and services (e.g., work of policemen, ﬁreﬁghters, etc...) at the
federal, state and local government level. Valuing goods is easy because there is
a market price. But how do we value the services of the police since one cannot
privately buy them? NIPA value them at cost, i.e. based on the wages paid
to employees (policemen, ﬁreﬁghters,...). Note that G does not include transfers,
such as Food Stamps or Unemployment Insurance because there is no production
associated to a transfer.

Example 1 A car can be private consumption, if bought by a household, in-
vestment, if bought by a ﬁrm that uses it for deliveries or even a government
expenditure if purchased by a government agency. So it is not the good itself that
makes it C,I or G, but rather its use.

• Exports E are deliveries of US goods (e.g., Ford car manufactured in Detroit
and sold to France) and services (e.g., ﬂight sold by USAIR to French citizen) to
the rest of the world

• Imports M are purchases of foreign goods (e.g., French cheese, Prada shoes)
and services (e.g., ﬂight sold by AirFrance to a US resident) by US households.

In billions of dollars, in the year 2002, the various components of aggregate expen-
ditures were, approximately:

Y = 10, 000, C = 7, 000, I = 1, 500, G = 1, 500, E = 1, 000, M = 1, 000

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To understand where Y = 10, 000 comes from, keep in mind that the population of the
U.S. is roughly 290 millions and income per capita is \$36,000.

Remark 2 The diﬀerence of exports minus imports (E − M) is called trade (or current
account) balance.

INCOME APPROACH
According to the income approach, GDP is calculated as the sum of all types of
income received by US households in a given period. These various forms of income
include:

• Compensation of employees: wages, salaries and fringe beneﬁts (68% of total income)

• Corporate proﬁts: proﬁt earnings of incorporated companies (12%)

• Proprietor’s income: earnings of the self-employed (e.g., law ﬁrm, small busi-
nesses) (11%)

• Rental Income: rents received by house owners from their tenants (2%)

• Net interest: interests paid on US bank accounts (7%)

Useful concepts in macroeconomics are the labor share, and the capital share
of income, computed as:
labor income
labor share =              ,
total income
capital income
capital share =                .
total income
Labor income is the sum of employees’ compensation plus a fraction of proprietor’s
income. Capital share is the sum of the residual fraction of proprietors’ income, cor-
porate proﬁts, net interests and rental income. The labor share of income is around
70% of total income, the capital share around 30%.

The sum of these ﬁve components gives National Income (NI). How do we get from
NI back to GDP? Below, we explain the necessary steps.

NI + Sales Taxes = Net National Product (NNP)
NNP + Capital Depreciation = Gross National Product (GNP)
GNP- U.S. Income earned Abroad + U.S. Income paid Abroad = Gross Domestic Product (GDP)

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There are some American citizens who live abroad whose income contributes to
National Product but not to Domestic Product, and some foreigners that have earnings
in the U.S. whose income is part of domestic income but not National Income. Similarly
for ﬁrms: there are US companies abroad and foreign companies in the US. So GNP
is the sum of all income paid to Americans, while GDP is the sum of all income paid
(and goods/services produced) in America.
Why are these three approaches equivalent? Every ﬁnal good that is sold and
purchased in the economy (and shows up as expenditure) has to be produced, and
those who participate to the production process have to be remunerated accordingly
through income (salaries of workers, proﬁts of ﬁrm’s owners, rental income of plants’
owners, interest rate on owners of ﬁnancial capital, etc...).

F IGURE ON CIRCULAR F LOW

GDP is a very good measure of production for all market transactions. But there
are a large quantity of transactions that do not occur through markets, hence they go
unmeasured.
First, home-production: cleaning, washing, cooking and childrearing at home are
all activities that produce a service. If they were purchased on the market, through
domestic workers, babysitters, etc., would be priced and included in GDP. When they
are generated at home, they escape national accounts. Since women have increased
their labor force participation substantially in the last 30 years, it is possible that now
homeproduction is much smaller than it used to be, but then perhaps true output
growth over the past 40 years is overestimated. Some oﬃcial estimates set the value of
home production at 10% of current GDP.
Second, the underground economy: activities ranging from hiring a domestic worker
oﬀ the books to the production of illegal drugs are not captured by national accounts
even though they generate output and income.

1.2    Saving-Investment Identity in Closed Economy
Savings are deﬁned as aggregate income minus private consumption, minus government
consumption expenditures, summarized in the equation below.

St = Yt − Ct − Gt .                                 (3)

More precisely, within aggregate savings, we need to distinguish three sources of
savings:

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• Households savings: Sh = Y − UP ROF + INT Dh − Th + T Rh − C

• Business savings: Sb = P ROF − Tb + T Rb

• Government savings: Sg = Th + Tb − INT Dh − T Rh − T Rb − G

where Y denotes GNP, UP ROF denotes proﬁts not distributed to households,
INT D denotes interests paid on government debt to households, T denotes taxes,
and T R denotes government transfers; moreover, the subscripts h, b, g denote respec-
tively households, business and government. Note that the business sector is the one
generating the highest amount of savings, through corporate proﬁts.

Remark 3 Household income net of taxes is called household disposable income, i.e.
available for expenditures and savings.

Remark 4 When the government receipts (Th + Tb ) are less (more) than government
outlays (INT Dh + T Rh + T Rb + G), we call government’s savings a budget deﬁcit
(surplus).

Recall that the fundamental national accounting equation, in closed economy, is

Yt = Ct + It + Gt ,                                (4)

hence substituting (4) into (3), we arrive to a very important equation:

It = St + (Mt − Et ) .

What does this equation mean? Let’s start by assuming a closed economy, i.e. an
economy without economic relations with the rest of the world (no imports and ex-
ports). In every period t (e.g., year), aggregate savings equal aggregate investments.
All income which is not consumed by private households or the government is saved,
and savings are used to ﬁnance national investments. In an open economy, there is an
additional way to ﬁnance investments, if It > St and the nation does not have enough
saving: get the funds from the rest of the world. In this case, like the US are doing
currently, the country runs a current account deﬁcit.

1.3    The Balance Sheet of Households
Just like ﬁrms, households have their own balance sheets including assets and liabilities.
The Table below looks at them in detail.

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ASSETS             50, 000             LIABILITIES        8, 000
Real Estate          15, 000           Mortgages             5, 500
Financial Wealth     35, 000           Credit Cards Debts    1, 500
Deposits           5, 000         Other loans           1, 000
Bonds              2, 500
Equities           18, 500
Pension Funds      9, 000
Billion of 2002 \$
An interesting point to make, in relationship to the discussion on savings above is
on the classiﬁcation of capital gains and losses, deﬁned as the change in the market
value of assets and liabilities, e.g. appreciation of owned home residence, decline in the
value of the owned stocks, etc.. Capital gains (and windfall gains from lotteries) made
by households are counted as increases in assets rather than savings, and as such they
show up in the balance sheet of households, not in the NIPA.
Note instead that capital gains made by ﬁrms, such as gains realized in the ﬁrms’
ﬁnancial portfolio are counted as corporate proﬁts, thus are recorded in the NIPA.
Some economists argue that households’ capital gains an losses should be counted
as income, since they are “perceived” as such and in fact they tend to aﬀect saving
behavior: in times of large capital gains like the 1990’s, households decrease their
savings.

1.4    Real GDP as a measure of living standards
Nominal GDP changes between year t and year t + 1 because diﬀerent amounts of
goods and services are produced between the two years, and because such goods and
services are sold at diﬀerent prices in the two years.
However, standards of living are determined by the quantities of goods and services
produced and consumed by households, not by the nominal value they have in the
market. As a consequence, it is not very useful to compare nominal GDP across
diﬀerent years, since it GDP could increase or decrease only because of changes in the
price level, even though quantities did not change.
To make comparisons over time, it is useful to introduce the notion of real GDP Yt .

Deﬁnition 1 Real GDP Yt is the sum of all ﬁnal goods and services produced in an
economy in period t valued at the prices of a certain base-year (or reference year) 0

X
I
Yt =         pi0 qit
i=1

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For example, consider two observations for real GDP at time t and at time t + 1

X
I
Yt =          pi0 qit ,
i=1
XI
Yt+1 =         pi0 qi,t+1 ,
i=1

and notice that prices at which the goods and services are valued are the same ones,
those of the reference year. The ﬁxed reference year for prices avoids contaminating
the comparison between GDP’s with changes in the price level between t and t + 1. In
fact, if we compare the two numbers above they only diﬀer because of the change in
the quantity of goods and services produced.

Remark 5 If we are interested in quantities, why don’t we just sum quantities and
forget about prices altogether? You cannot sum 2 apples, 1 car and 3 plane tickets:
what’s the result? We need prices to convert all goods and services in \$ and aggregate
them together.

The growth rate of real GDP between t and t + 1 is
Yt+1 − Yt   103 − 100
gy (t, t + 1) =             =           = .03 = 3%
Yt          100
When the press writes: “GDP increased by 1% this last quarter”, usually they refer
to real GDP.

1.5    Measurement of Prices
There are at least two important price indexes to learn about: 1) the GDP deﬂator and
2) the Consumers’ Price Index (CPI). Price indexes describe the evolution of the price
level for a given “basket of goods” which is somewhat representative or interesting.
Let us start from the GDP deﬂator.

Deﬁnition 2 The GDP deﬂator is the ratio of nominal to real GDP in a given year t
PI
i=1 pit qit
P0,t = PI
i=1 pi0 qit

The GDP deﬂator tells us how much the price level of the basket of ﬁnal goods and
services produced in period t in the economy increased from the base (or reference) year
0. The GDP deﬂator is based on all goods produced in the economy, even investment
goods (such as trucks, planes, oil pipes) which are not of interest to households.

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When prices increase, the purchasing power of households falls. To get a fair as-
sessment of how much it falls, we need to restrict our attention to the typical basket of
goods and services purchased by the representative household. This is the role of the
CPI.

Deﬁnition 3 The Consumers’ Price Index (CPI) is
PJ
j=1   pit qj0
CP It = PJ
j=1   pi0 qj0

i.e. the CPI is the ratio between the time t and the time 0 value of the typical
basket of goods purchased by households at time 0. Time 0 is called the base year.
The change in the CPI is used to measure “inﬂation”.

Deﬁnition 4 The inﬂation rate measures the change in the CPI between time t and
time t + 1
PJ
CP It+1 − CP It   CP It+1       j=1 pi,t+1 qj0
π t,t+1 =                 =         − 1 = PJ             −1
CP It         CP It          j=1 pit qj0

The inﬂation rate is a very important macroeconomic indicator. The Federal Re-
serve Bank watches it and decides its monetary policy strategy based on the current
and expected inﬂation rate; the stock market reacts to changes in inﬂation; many social
security and welfare beneﬁts are indexed to the CPI, through a measure of the cost of
living of American families called COLA (COst of Living Adjustment).
There is a diﬀerence between the deﬁnitions of the GDP deﬂator and the CPI. More
in general, there are two types of price indexes:

• Laspeyres Index:                           P
pit qi0
L0,t    = Pi         .
i pi0 qi0
This price index measures the change in the price level between 0 and t of the
basket of goods produced at time 0, which is kept ﬁxed.

• Paasche Index                              P
pit qit
P0,t   = Pi         .
i pi0 qit
This price index measures the change in price between 0 and t of the basket of
goods produced at time t.

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Clearly, the CPI is a Laspeyres index, whereas the GDP deﬂator is a Paasche index.
The diﬀerence is what basket of goods we use in our calculation. Is it best to use the
same one (of the reference year), or the one at time t which changes period by period?
Suppose we choose the Laspeyres index and take the time-zero basket ﬁxed. Sup-
pose that there is an oil-shock (like in the 1970s) at time 0 and the price of oil skyrockets,
households reduce the demand for gasoline and cars and increase the use of substitute
means of transportation, like the subway. Then, at time t the actual basket of goods
includes much less gasoline than at time zero. But the Laspeyres formula does not take
it into account, so it will overstate inﬂation. It is easy to see that the Paasche tends
to understate inﬂation instead, because it gives a small weight to gasoline (it gives it
the time t share of expenditures). This problem is called substitution bias, because
the origin of the lack of precision is the fact that ﬁrms and households substitute away
from expensive goods into cheap goods and the composition of the basket changes.
But if the limit of the Laspeyres index is that the weights qi are ﬁxed, whereas the
limit of the Paasche index is that they are variable, but they change too fast, can we
use a combination of them and construct an ideal price index? This is a long-standing
problem in economics: the so-called “chain-weighted” indexes are the price indexes
that come closer to the solution. Chain-weighted indexes basically use a rolling base-
year. The BEA has recently switched from ﬁxed-base year (Laspeyres type) indexes to
chain-weighted indexes, re-issuing all the historical data in this new format.
Another problem with the measurement of prices is that of quality improvements.
Consider Personal Computers (PC’s). The average dollar price of a PC now is the
same as (maybe even lower than) ten years ago. But can we say that a typical PC
produced now is the same as one produces a decade ago? Not really. An orange
is always an orange, but the quality of technologically-intensive goods changes very
quickly. Computers have larger hard-disks, larger memory, faster processors, better
videos, and so on. In this sense, a PC is much cheaper today. This problem is called
quality-bias. For example, suppose the price of a computer in 1993 and in 2003 has
always been \$1,000. The standard PC in 2003 has 256 MB of RAM, while in 1993 it
used to have only 128 MB. This means that if we keep “constant” the quality of PC
throughout the last decade, the price of PC has fallen by 50%! The methodology that
calculates prices of baskets with constant-quality is called “hedonic price technique”.
Finally, we have the problem due to the introduction of new goods. Consider
mobile phones: they are part of the basket of goods purchased by a typical American
family. But, what was the price of a mobile phone in 1950 when the good did not

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exist? Notwithstanding the importance of mobile phones today, one cannot include
the mobile phones in a basket of goods when comparing the price level in the US in
1950 with the price level of the same group of goods in 2000.
Recently the use of chain-weighted indexes, and other techniques to minimize prob-
lems associated to quality improvements and introduction of new goods has been ad-
vocated by the Boskin Commission Report (1996). The Commission concluded that,
once all the biases are properly corrected, the inﬂation rate in the U.S. could have been
overestimated by half to one percentage point per year in the past 50 years.

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