# Measurement

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```					                    Measurement Economics
ECON4700
Mid term Exam
February 14, 2011
Professor: Marc Prud’Homme

Instructions

1.   You have 90 minutes to complete the exam.
2.   Choose 4 of the 5 questions
3.   Answer all questions in the exam booklet.
4.   All questions have a weight of 25 %
7.   Success to you!

1. Explain the difference between the axiomatic (or test)
approach and the economic approach for choosing the
best price index.

The purpose is to pick the best index formula. How do we go about
that? Two approaches have ben proposed:
1- The axiomatic approach
2- The economic approach

Must present some of the tests that are used such as the one
presented in class.

The axiomatic approach to the selection of an appropriate index
formula specifies a number of desirable properties an index
formulation should possess.

Seeks to determine the most appropriate functional form for an
index by specifying a number of axioms, or tests, that an index
ought to satisfy.

Potential indexes are then evaluated against the specified
properties and the index that passes the most tests is the
preferred one.

1. Positivity: the price index and its constituent vectors of
prices and quantities should be positive.
2. Identity test: If the price of every product is identical in
both periods, then the price index should be equal to unity,
regardless of the quantity vector.
3. Proportionality in current prices: if all prices in period t
are multiplied by the positive number x, then the new price
index should be x times greater than the old price index; i.e.,
the price index function is (positively) homogeneous of degree
one in the components of the period t price vector.

Measurement Economics: Mid-term Exam                     February 2011
4. Invariance to changes in units of measurement (commensurability
test): the price index does not change if the units in which
the products are measured are changed.
5. Time reversal test: if all the data for the two periods are
interchanged, then the resulting price index should equal the
reciprocal of the original index.
6. Mean value test for prices: the price index lies between the
highest and the lowest price relatives.
7. Paasche and Laspeyres bounding test: the price index lies
between the Paasche and Laspeyres price indices.
8. Monotonicity test: if any period t price is increased, then the
price index must increase.

More important ones:

Commensurability test

Time reversal test

Remember that with the axiomatic approach, prices and quantities
were treated as separate independent variables.

Two price vectors and two quantity vectors
With the economic approach, the quantities are a function of the
prices.

Two price vectors plus a functional relationship connecting the
prices to the quantities in periods 1 and 2 respectively.

Parameters of the function are unknown hence economic theoretic
indices cannot be estimated

Two main functions relating Qs to Ps:

Utility functions
Production functions

Or the generic: “aggregator function”
The classic example of an economic theoretic index is the Cost-of-
living-index (COLI).

COLI: “the ratio of the minimum expenditures required to attain a
particular indifference curve (level of welfare) under two price
regimes or situations”.

Graph COLI

Paasche:           understate COLI
Laspeyres:   overstate COLI

Measurement Economics: Mid-term Exam                  February 2011
2. Briefly describe what a Consumer Price Index (CPI) is.
What are some of the weaknesses associated with most if
not all CPIs produced by national statistical agencies?
Explain.

3. Name and show 6 index number formulae that were either
presented in class or covered in the assignments.

4. Looking to the future, it is possible to identify
certain trends in the demand for economic statistics
that will presumably strengthen in the years to come.
Name 4 of those trends with a brief explanation for
each.

In the world of business, medium-to-large companies are interested
in receiving timely information not only about national and
international macroeconomic developments, but also on various
aspects concerning the sectors in which they operate, at a
meaningful level of territorial detail. By contrast, small
businesses want information more limited in scope, possibly
relating to the local market in which they work, or to their own
sector of economic activity. Then there are research centres,
either public or private, whose needs for information go in all
directions, depending on the subject matter. Lastly, households
mainly want information that is quite general (or “curious”),
expressed in a form they can understand, almost exclusively
“consumed” via the different media (television, the press,
Internet, etc.).

-   Service sector
-   Measurement of “intangible” activities.
-   Exchange of data
-   Increase for the demand for micro-data (single units).
-   Greater integration of economic, social and environmental
statistics will lead to new integrated accounting frameworks
capable of bringing together these three main themes, mainly to
enable policies that make economic growth socially and
environmentally sustainable
-   The increasing role of large emerging countries, such as China,
Russia, Brazil, is putting pressure on international
organisations to produce more comparable statistics.
-

5. (Note that the following questions are mutually
exclusive)
a. The article: Time Well Spent states that the Cost
of living is going up but then seems to go in the

Measurement Economics: Mid-term Exam                   February 2011
opposite direction with its thesis, that we are
better off today than before. Please explain this
divergence.
b. What is the Index Number Problem?
c. Define the Consumer Price Index and explain what
it is trying to measure in the case of the

Measurement Economics: Mid-term Exam          February 2011

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