Example 1 Index Number - UWCENTRE

1

Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.olivierdejong.com

Valua%onandpricing(November5,2013)

Lecture3

IndexNumbers

10/8/16, 2:46 AM

of 1https://targetcareers.co.uk/sites/targetcareers.co.uk/files/public/Bangor.jpg

2

GOALS

l  Describe the term index. l  Understand the difference between a weighted and

an unweighted index. l  Construct and interpret a Laspeyres price index. l  Construct and interpret a Paasche price index. l  Construct and interpret a value index. l  Explain how the Consumer Price Index is

constructed and interpreted.

20-3 Copyright © 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e

Introduction

•  An index number is a statistical value that measures the change in a variable with respect to time

•  Two variables that are often considered in this analysis are price and quantity

•  With the aid of index numbers, the average price of several articles in one year may be compared with the average price of the same quantity of the same articles in a number of different years

•  There are several sources of ‘official’ statistics that contain index numbers for quantities such as food prices, clothing prices, housing, wages and so on

4

Index Number – Example 1

According to the Bureau of Labor Statistics, in January 1995 the average hourly earnings of production workers was $11.47. In June 2005 it was $16.07.

What is the index of hourly earnings of production workers for June 2005 based on January 1995?

5

An index can also compare one item with another. Example: The population of the Canadian province of

British Columbia in 2004 was 4,196,400 and for Ontario it was 12,392,700. What is the population index of British Columbia compared to Ontario?

Index Number –Example 2

6

Why Convert Data to Indexes?

l  An index is a convenient way to express a change in a diverse group of items.

–  The Consumer Price Index (CPI), for example, encompasses about 400 items—including golf balls, lawn mowers, hamburgers, funeral services, and dentists’ fees. Prices are expressed in dollars per pound, box, yard, and many other different units. Only by converting the prices of these many diverse goods and services to one index number can the federal government and others concerned with inflation keep informed of the overall movement of consumer prices.

l  Converting data to indexes also makes it easier to assess the trend in a series composed of exceptionally large numbers.

–  For example, total U.S. retail sales for the month of July 2005 were $357,013,000. For July 2004, the total retail sales were $323,604,000. This increase of $33,409,000 appears significant. Yet if the July 2005 retail sales are expressed as an index based on July 2004 retail sales the increase is 10.3 percent.

2

7

Indexes

l  In many situations we wish to combine several items and develop an index to compare the cost of this aggregation of items in two different time periods.

–  For example, we might be interested in an index for items that relate to the expense of operating and maintaining an automobile. The items in the index might include tires, oil changes, and gasoline prices.

–  Or we might be interested in a college student index. This index might include the cost of books, tuition, housing, meals, and entertainment.

l  There are several ways we can combine the items to determine the index.

8

Indexes

l  Unweighted Indexes –  Simple Average of the Price Indexes –  Simple Aggregate Index

l  Weighted Indexes –  Lespeyres Price Index –  Paasche Price Index

l  Fisher’s Price Index l  Value Index l  Special Purpose Index

–  Consumer Price Index –  Producer Price Index –  S&P Index

9

Unweighted Indexes

10

Laspeyres versus Paasche Index

When is Laspeyres most appropriate and when is Paasche the better choice?

l  Laspeyres –  Advantages Requires quantity data from only the base period. This

allows a more meaningful comparison over time. The changes in the index can be attributed to changes in the price.

–  Disadvantages Does not reflect changes in buying patterns over time. Also, it may overweight goods whose prices increase.

l  Paasche –  Advantages Because it uses quantities from the current period, it

reflects current buying habits. –  Disadvantages It requires quantity data for the current year.

Because different quantities are used each year, it is impossible to attribute changes in the index to changes in price alone. It tends to overweight the goods whose prices have declined. It requires the prices to be recomputed each year.

11

Simple Average - Example

12

Simple Aggregate Index – Example

3

13

Weighted Indexes

14

Value Index

l  A value index measures changes in both the price and quantities involved.

l  A value index, such as the index of department store sales, needs the original base-year prices, the original base-year quantities, the present-year prices, and the present year quantities for its construction.

l  Its formula is:

15

The prices and quantities sold at the Waleska Clothing Emporium for various items of apparel for May 2000 and May 2005 are:

Value Index - Example

What is the index of value for May 2005 using May 2000 as the base period?

16

Value Index - Example

17

Consumer Price Index

The U.S. Bureau of Labor Statistics reports this index monthly. It describes the changes in prices from one period to another for a “market basket” of goods and services.

18

Producers Price Index

l  Formerly called the Wholesale Price Index, it dates back to 1890 and is also published by the U.S. Bureau of Labor Statistics.

l  It reflects the prices of over 3,400 commodities. Price data are collected from the sellers of the commodities, and it usually refers to the first large-volume transaction for each commodity. It is a Laspeyres-type index.

4

19

CPI Uses

l  It allows consumers to determine the effect of price increases on their purchasing power.

l  It is a yardstick for revising wages, pensions, alimony payments, etc.

l  It is an economic indicator of the rate of inflation in the United States.

l  It computes real income: real income = money income/CPI X (100)

20

CPI Uses - Formulas


20.2 Simple index numbers

•  We will examine index numbers that are constructed from a single item only

•  Such indexes are called simple index numbers •  Current period = the period for which you wish to find

the index number •  Base period = the period with which you wish to

compare prices in the current period •  The choice of the base period should be considered

very carefully •  The choice itself often depends on economic factors

1. It should be a ‘normal’ period with respect to the relevant index

2. It should not be chosen too far in the past


20.2 Simple index numbers (cont…)

•  The notation we shall use is: –  pn = the price of an item in the current period –  po = the price of an item in the base period

•  Price relative –  The price relative of an item is the ratio of the price of the

item in the current period to the price of the same item in the base period

–  The formal definition is:

o

n

pprelativePrice =


20.2 Simple index numbers (cont…) •  Simple price index

–  The price relative provides a ratio that indicates the change in price of an item from one period to another

–  A more common method of expressing this change is to use a simple price index


100pp

100relativepriceindexpriceSimple

o

n ×=

×=


20.2 Simple index numbers (cont…)

•  The simple price index finds the percentage change in the price of an item from one period to another

–  If the simple price index is more than 100, subtract 100 from the simple price index. The result is the percentage increase in price from the base period to the current period

–  If the simple price index is less than 100, subtract the simple price index from 100. The result is the percentage by which the item cost less in the base period than it does in the current period

5


20.3 Composite index numbers

•  A composite index number is constructed from changes in a number of different items

•  Simple aggregate index –  the simple aggregate index has appeal because its nature

is simplistic and it is easy to find –  The formal definition is:

Where Σpn = the sum of the prices in the current period Σpo = the sum of the prices in the base period

100p

pindexaggregateSimple

o

n×=

∑∑


20.3 Composite index numbers (cont…)

•  Simple aggregate index (cont…) –  Even though the simple aggregate index is easy to calculate, it

has serious disadvantages: 1. An item with a relatively large price can dominate the

index 2. If prices are quoted for different quantities, the simple

aggregate index will yield a different answer 3. It does not take into account the quantity of each item sold

–  Disadvantage 2 is perhaps the worst feature of this index, since it makes it possible, to a certain extent, to manipulate the value of the index


20.3 Composite index numbers (cont…)

•  Averages of relative prices –  This index also does not take into account the quantity of

each item sold, but it is still a vast improvement on the simple aggregate index


where k = the number of items pn = the price of an item in the current period po = the price of an item in the base period

k

100pp

pricesrelativeofAverage o

n∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛×

=


20.4 Weighted index numbers

•  The use of a weighted index number or weighted index allows greater importance to be attached to some items

•  Information other than simply the change in price over time can then be used, and can include such factors as quantity sold or quantity consumed for each item

•  Laspeyres index –  The Laspeyres index is also known as the average of

weighted relative prices –  In this case, the weights used are the quantities of each item

bought in the base period


20.4 Weighted index numbers (cont…)

–  The formula is:

Where: qo = the quantity bought (or sold) in the base period pn = price in current period po = price in base period –  Thus, the Laspeyres index measures the relative change in

the cost of purchasing these items in the quantities specified in the base period

100index Laspeyres ×=∑∑

oo

on

qpqp


20.4 Weighted index numbers (cont…) •  Paasche index

–  The Paasche index uses the consumption in the current period

–  It measures the change in the cost of purchasing items, in terms of quantities relating to the current period

–  The formal definition of the Paasche index is:

Where: pn = the price in the current period po = the price in the base period qn = the quantity bought (or sold) in the current period

100qp

qpindexPaasche

no

nn×=

∑∑

6



•  Comparison of the Laspeyres and Paasche indexes

–  The Laspeyres index measures the ratio of expenditures on base year quantities in the current year to expenditures on those quantities in the base year

–  The Paasche index measures the ratio of expenditures on current year quantities in the current year to expenditures on those quantities in the base year

–  Since the Laspeyres index uses base period weights, it may overestimate the rise in the cost of living (because people may have reduced their consumption of items that have become proportionately dearer than others)



•  Comparison of the Laspeyres and Paasche indexes (cont…)

–  Since the Paasche index uses current period weights, it may underestimate the rise in the cost of living

–  The Laspeyres index is usually larger than the Paasche index

–  With the Paasche index it is difficult to make year-to-year comparisons, since every year a new set of weights is used

–  The Paasche index requires that a new set of weights be obtained each year, and this information can be expensive to obtain

–  Because of the last 2 points above, the Laspeyres index is the one most commonly used



•  Fisher’s ideal index –  Fisher’s ideal index is the geometric mean of the Laspeyres

and Paasche indexes –  Although it has little use in practice, it does demonstrate the

many different types of index that can be used –  The formal definition is:

( )( )

100qpqp

qpqp

indexPaascheindexLaspeyresindexsFisher'

nooo

nnon×=

=

∑∑∑∑


20.5 The Consumer Price Index (CPI) •  The measure most commonly used in Australia as a general

indicator of the rate of price change for consumer goods and services is the consumer price index

•  The Australian CPI assumes the purchase of a constant ‘basket’ of goods and services and measures price changes in that basket alone

•  The description of the CPI commonly adopted by users is in terms of its perceived uses; hence there are frequent references to the CPI as –  a measure of inflation –  a measure of changes in purchasing power, or –  a measure of changes in the cost of living


20.5 The Consumer Price Index (CPI) (cont…) •  The CPI has been designed as a general measure of price

inflation for the household sector. •  The CPI is simply a measure of the changes in the cost of a

basket, as the prices of items in it change •  From the September quarter 2005 onwards, the total basket has

been divided into the following 11 major commodity groups: –  food –  alcohol and tobacco –  clothing and footwear –  housing –  household contents and services –  health –  transportation –  communication –  research –  education –  financial and insurance services


20.5 The Consumer Price Index (CPI) (cont…)

•  Historical details of the CPI –  Retail prices of food, other groceries and average rentals of

houses have been collected by the ABS for the years extending back to 1901

–  From its inception in 1960, the CPI covered the six state capital cities. In 1964 the geographical coverage of the CPI was extended to include Canberra. From the June quarter in 1982 geographic coverage was further extended to include Darwin

–  Index numbers at the ‘Group’ and ‘All groups’ levels are published for each capital city and for the weighted average of eight capital cities

7



•  The conceptual basis for measuring price changes

–  The CPI is a quarterly measure of the change in average retail price levels

–  In measuring price changes, the CPI aims to measure only pure price changes

–  The CPI is a measure of changes in transaction prices, the prices actually paid by consumers for the goods and services they buy

–  It is not concerned with nominal, recommended or list prices –  The CPI measures price change over time and does not

provide comparisons between relative price levels at a particular date



•  The index population –  Because the spending patterns of various groups in the

population differ somewhat, the pattern of one large group, fairly homogeneous in its spending habits, is chosen for the purpose of calculating the CPI

–  The CPI population group is, in concept, metropolitan employee households

–  For this purpose, employee households are defined as those households that obtain the major part of their household income from wages and salaries


20.5 The Consumer Price Index (CPI) (cont…) •  Collecting prices

–  This involves collecting prices from many sources, including supermarkets, department stores, footwear stores, restaurants, motor vehicle dealers and service stations, dental surgeries, etc.

–  In total, around 100 000 separate price quotations are collected each quarter

–  Prices of the goods and services included in the CPI are generally collected quarterly

–  The prices used in the CPI are those that any member of the public would have to pay on the pricing day to purchase the specified good or service

–  Any sales or excise taxes that the consumer must pay when purchasing specific items are included in the CPI price



•  Periodic revision of the CPI –  The CPI is periodically revised in order to ensure it continues

to reflect current conditions –  CPI revisions have usually been carried out at approximately

5-yearly intervals

•  Changes in quality –  it is necessary to ensure that identical or equivalent items are

priced in successive time periods –  This involves evaluating changes in the quality of goods and

services


20.6 Using the CPI

•  There are a number of situations where the CPI is used to make adjustments to prices charged and payments made

•  Examples include changes in rent, pension payments and child support payments

•  Such adjustments are often made by the relevant government agency, but if members of the community wish to use the CPI for such purposes, it is their responsibility to ensure that this index is suitable


20.7 Index numbers as a measure of deflation

•  One of the uses for price indexes is to measure the changes in the purchasing power of the dollar

•  This is known as deflation •  In order to eliminate the effect of inflation and obtain a clear

picture of the ‘real’ change, the values must be deflated •  For example, to deflate an actual salary and express it in

terms of ‘real’ salary (of the base year), use:

yearcurrentin CPIyearbaseinCPIyearcurrentinsalaryactualsalaryReal'' ×=

8

43 of 46 Copyright © 2010 Pearson Education, Inc. · Economics · R. Glenn Hubbard, Anthony Patrick O’Brien, 3e.

Cha

pter

3:

Whe

re P

rices

Com

e Fr

om: T

he In

tera

ctio

n of

Dem

and

and

Sup

ply

¡  Read Quantitative Methods-module guide. ¡  Any questions please e-mail: [email protected]

¡  … and make notes as you do so, in whatever way works best for you

in terms of remembering information (your performance on this course is only assessed by exam).

Remember

Example 1 Index Number - UWCENTRE

Documents

Transcript of Example 1 Index Number - UWCENTRE