ISP 120 Week 7

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ISP 120 Week 7

• Consumer Price Index

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Assignment 4

• Read the article "Chicago falls out of 1st in
  murders" by David Heinzman from the Chicago
  Tribune, Jan. 1, 2003.
• Does the headline "Chicago falls out of 1st in
  murders" refer to an absolute quantity or a
  relative quantity?  In other words, did Chicago
  fall out of first in absolute terms or in
  relative terms?  Briefly explain.  

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• In the second paragraph, the author states that
  "Chicago was way ahead of the pack in the murder
  rate..."   According to the article, what is the
  "pack" that Chicago is ahead of?
• Chicago, New York, and LA

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• Let us look more carefully at the complete 2001
  data. (This is the data for the year before the
  article) 
• Open the file HomicidesForCities2001.xls.  Sort
  the data by the absolute number of murders. 
  Which three cities had the highest number of
  murders in 2001?
• Chicago, New York, LA

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• In Column D, calculate the homicide rate
  (homicides per person).  Paste into your Word
  document the top five rows of the resulting
  table.
• Now sort the data by column D.  Which three
  cities had the highest murder rates in 2001?
• Fairfield, Alabama (.000965)
• Gary, Indiana (.000794)
• Opa Locka, Florida (.000652)

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• How many times greater was the murder rate for
  the Fairfield, Alabama than the rate for Chicago?
  
• .000965/.000228 4.23 times greater
• There were exactly four cities with population
  greater than 500,000 with a rate higher than
  Chicago's.  Which were they?

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• Now sort by column B (population) in descending
  order to look at the largest cities in the US. 
  Copy the top 10 rows of the table and paste them
  into a different part of your Excel sheet.  You
  should now have the just the cities with
  population greater than 1 million.  Sort this
  table by rate and paste the resulting table into
  your Word document.  Who is "ahead of the pack"
  here when we consider cities of population 1
  million or greater?

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•  What was the overall impression of the article
  and the accompanying graph?   Given the
  additional data in the Excel file, do you think
  the article is misleading in certain ways? If so,
  how?  Critique the use of quantitative
  information in the New Year's Day article.
• The article refers to the actual number of
  murders and the murder rate per 100,000 people in
  the 3 largest cities. This leads the audience to
  believe that they are the most dangerous cities
  that have the highest rate or number of murders.
  They do have the highest number of murders,
  however, they do not have the highest murder
  rates. Chicago actually ranks 56th in highest
  murder rate.

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Week 7 Goals

• Become aware of the changing value of money and
  the need to measure it
• Learn how the CPI is created from price data and
  how the inflation rate is calculated
• Learn how to compare prices of products in two
  different years
• Learn how to convert an entire times series of
  price data into constant dollars
• Become aware of the econometric controversy
  regarding the potential bias of the CPI toward
  overstating inflation and some of possible
  implications of this bias

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• What are some prices you remember that have
  changed in your lifetime?
• How much were they then?
• How long ago was it?
• How much are they now?
• See The Consumer Price Index

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Item Percentage Increase in Price

• Hershey bar - 1180
• New York Times - 1100
• First class postage - 700
• Gasoline (gallon) - 284
• Hamburger (McDonald's double) - 861
• Chevrolet (full size) - 790
• Refrigerator freezer - 60

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Observations

• Hershey bars have really gone up, but
  refrigerator freezers haven't.
• Surprisingly, gasoline didn't go up nearly as
  fast as McDonald's hamburgers or cars.
• What complications come to mind about the car and
  freezer data?

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• A car in 1998 is going to be safer, more
  dependable, more comfortable, less expensive to
  run and maintain than a car in 1962
• A freezer in 1998 was probably significantly
  better than the 1962 model in terms of ease of
  use and efficiency
• Therefore, it is unclear if the prices of cars
  and freezers from 1962 and 1998 are really
  comparable

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What can we learn from this handful of items and
prices?

• Prices can and do change dramatically in
  relatively short periods, so much so that a price
  in the past virtually meaningless to us unless we
  compare it to other prices of the time.
• Prices of items do not go up consistently some
  prices go up faster than others.  
• Items change over time so that it becomes
  difficult to compare prices because the items are
  not really comparable.

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Index Numbers

• The tool that economists use to compare prices of
  the past and to measure inflation is called the
  consumer price index (CPI)
• The CPI is an example of an index number
• An index number is a derived quantity that
  describes the ratio of a quantity and its value
  at a base period (or its values at a standard)

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• The base period index is typically set to 100 so
  that percentage increases from the base period
  can be almost instantly inferred.
• Index numbers are most commonly used for time
  series, so looking at index numbers in that
  situation is a good place to start in learning
  about them

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• To create a White Bread Index, we would choose a
  base year and set the index equal to 100 in that
  year.  We use the very odd "equation" 1980100 to
  signify our choice of 1980 as a base year

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We want the index to reflect the ratio of bread
prices from a given year to the price in 1980. 
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• Now we can fill the table

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• What is so useful about the index number table is
  that we can immediately read off the percentage
  change in the price from the base year. 
• For example,  in 1996, the index was 172.1. 
  172.1 is 72.1 higher than 100, so we can
  conclude that white bread prices are 72.1 higher
  in 1996 than in 1980.  
• Similarly, in 1986, white prices were 11.0
  higher. 

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• Furthermore, with the index numbers we can
  calculate the percentage change in price for any
  two years (even without knowing the actual
  prices.
• For example, the percentage change in the price
  from 1989 to 1999 is (174.2-130.8)/130.8 33.1.
  

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Comparisons

• Another useful feature of indices is that if two
  indices have the same base year, we can readily
  make comparisons.
• The price index for local telephone service
  (1980100) in 1997 was 224.0
• The price index for intrastate long distance
  telephone calls (1980100) in 1997 was 110.2
• Local rates rose by 124 while intrastate rates
  only rose 10.2

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• We cannot compare indices from different base
  years
• The price index for coffee (1990100) in 1997 was
  143.0
• The price index for dairy products (1980100) in
  1997 was 160.1
• We cannot conclude that dairy prices have risen
  faster than coffee prices.
• We can conclude that dairy prices rose 60.1 from
  1980 to 1997, and coffee prices rose 43.0 from
  1990 to 1997

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• Finally, note that one can make indices for other
  data series besides for price
• sales, inventory levels, manufacturing activity

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The Consumer Price Index

• In the previous section, we saw how one can
  construct an individual price index
• When based in the same year, such indices make
  comparisons between prices straightforward
• But how would one measure general inflation?
• The problem is that individual prices go up by
  differing percentages. Some prices even go down.
• The solution that the Bureau of Labor Statistics
  has adopted is called a fixed market basket index

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• In 1919, the Bureau of Labor Statistics
  recognized the need for a systematic study of
  wages and prices
• Began publishing "cost of living" indices for 32
  large shipbuilding and industrial centers to
  assist in settling labor disputes
• Workers were insisting on higher wages to offset
  the higher cost of living that resulted from
  World War I
• Price indices give an "objective" measure of the
  cost of living and facilitate bargaining between
  unions and managers

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• Since then the scope of the price indices
  published by the Bureau of Labor Statistics has
  greatly broadened
• The indices continue to play an important role in
  labor negotiations but in addition are now used
  as escalation measures for entitlement programs
  such as
• social security, food stamps, welfare, Medicaid,
  and Medicare

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• The index affects the income of almost 80 million
  people
• 47.8 million Social Security beneficiaries
• about 4.1 million military and Federal Civil
  Service retirees and survivors
• about 22.4 million food stamp recipients
• Changes in the CPI also affect the cost of
  lunches for the 26.7 million children who eat
  lunch at school

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• Some private firms and individuals use the CPI to
  keep rents, royalties, alimony payments and child
  support payments in line with changing prices
• Since 1985, the CPI has been used to adjust the
  Federal income tax structure to prevent
  inflation-induced increases in taxes
• Because they have become so important, they have
  become controversial and even politically charged

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• In order to measure general price increases, the
  Bureau of Labor Statistics constructs an
  imaginary "market basket" of goods that an
  average family needs to lead an average life
• The market basket includes specific items
  relating to housing, food, transportation,
  medical care, clothing, entertainment, education
  and communication
• Currently, there are approximately 80,000 items
  in the "basket"

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• Price data for these items is collected monthly
  from 22,500 specific outlets and 7,300 specific
  housing units in 44 urban areas
• The prices for identical goods from the same area
  are averaged, and individual price indices are
  calculated for each item and geographic area
• Finally the individual price indices are in
  essence summed up to create the "price" of the
  entire market basket

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• The final price is actually a weighted sum, the
  weights reflecting the proportion that the
  average family spends on various categories and
  population of the geographic area
• The following table shows the current weightings
  for the broadest item categories

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• Category Weighting
• Housing 39.6
• Transportation 17.6
• Food 16.3
• Entertainment 6.1
• Medical Care 5.6
• Education/Communication 5.5
• Apparel and Upkeep 4.9
• Other 4.3

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• The CPI is the index number created from the
  "price" of the entire market basket
• Currently, the base "year" for the CPI is 1982-84
  
• This means that the average of the CPI over the
  three years 1982, 1983, and 1984 is set equal to
  100.

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Example of Construction of the CPI

• Our market basket will consist of
• one month's rent for a four room apartment
  (housing)
• one gallon of unleaded gasoline (transportation)
• one pound of white bread (food)
• one movie ticket (entertainment)
• one physician's visit (medical care)
• one ten minute long distance telephone call
  (communication)
• one pair of blue jeans (apparel)
• one month's refuse collection (other)

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• Finally we take the weighted average of the
  indices for the categories
• 110.039.6 95.517.6 101.416.3
  102.96.1 101.35.6 91.75.5 103.1 4.9
  103.1 4.3
• which yields 103.4.

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• The CPI created in this fashion is published
  monthly
• The market basket and the list of outlets undergo
  minor changes continually to adjust for products
  that change significantly or for outlets that
  close
• The market basket undergoes a major revision
  roughly every ten years

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• The Bureau of Labor Statistics actually publishes
  two CPI's, the CPI-U (All Urban Consumers) and
  the CPI-W (Urban Wage Earners and Clerical
  Workers).
• The Bureau of Labor Statistics estimates that the
  CPI-U represents about 87 of the total US
  population
• it is based on the expenditures of almost all
  urban residents including professionals, the
  self-employed, the poor, the unemployed, and
  retired persons.
• The spending patterns of rural dwellers, persons
  in the Armed Forces, and those in institutions
  (hospitals and prisons) are not included.

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• The CPI-W is based on the expenditures of urban
  households more than half of whose income comes
  from clerical or wage occupations
• The Bureau of Labor Statistics estimates that it
  represents about 32 of the US population
• We will use the CPI-U exclusively since it is
  represents the experiences of a larger proportion
  of the population
• Any reference to "CPI" will be to the CPI-U
  unless explicitly stated otherwise.

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The Official CPI since 1982
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What do these numbers mean?

• A common misunderstanding is to think that the
  CPI number is the price of the market basket in a
  given year
• While the CPI number is derived from the price of
  the market basket, it is actually unitless
• To be precise it is the ratio of the price of the
  market basket in a given year to the price in the
  base year multiplied by 100

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• However, the CPI can be thought of as the amount
  the average consumer would have to spend in a
  given year to buy the same basic goods and
  services that one would have to pay 100 for in
  the base period
• For example, on average in 1998, one would have
  to spend 163.00 to buy the same goods and
  services that one would have paid 100 for in the
  base period 1982-84
• Similarly, in 1994 one would have to spend
  148.20 to buy the same goods and services that
  one would have paid 100 for in the base period
  1982-84

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• Since each CPI number is equivalent to 100 in
  the base period, each CPI number is equivalent to
  every other one
• 163.00 in 1998 bought the same goods and
  services on average that would have cost 160.50
  in 1997
• 152.40 in 1995 bought the same goods and
  services on average as 124.00 did in 1990
• We can say that 152.40 1995 dollars is equivalent
  to 124.00 1990 dollars

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Constant Dollars

• The interpretation of the CPI in the last
  paragraph allows us to compare prices in two
  different years
• For example the price of gasoline in 1990 was
  1.16 per gallon on average
• In 1997, it averaged 1.23
• Was gasoline more expensive or less expensive in
  1997?

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• On the face of it, it seems that gas is more
  expensive in 1997
• To compare the prices taking into account the
  changing value of money, we convert one of the
  prices to the same year as the other
• Typically we convert forward to the more recent
  year

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• We want to convert 1.16 in 1990 dollars to its
  equivalent in 1997 dollars
• The CPI table tells us that 130.70 in 1990
  dollars is equivalent to 160.50 in 1997 dollars
• We wish to know
• 1.16 in 1990 dollars is equivalent to ? in 1997
  dollars

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• Set up the proportionality
• Solving this proportion we find that 1.16 in
  1990 was equivalent to 1.42 in 1997
• In other words, when Americans paid 1.16 per
  gallon for gasoline in 1990, it was equivalent to
  someone paying 1.42 in 1997, which is
  considerably more that what they were actually
  paying in 1997

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• So gasoline was significantly cheaper in 1997
  than it was in 1990
• Economists say that the equivalent price in a
  different year is in real or constant dollars
• In our example, economists will say that the
  price of gasoline in 1990 was 1.42 in constant
  1997 dollars
• The process of converting is often called
  converting to constant dollars

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Another use of the CPI is to convert an entire
series of price to constant dollars
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• Since the value of the dollar decreased each
  year, this graph is not a realistic depiction of
  electricity costs over this period
• To get a more accurate understanding, we convert
  the entire data series to constant 1998 dollars

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Freezing A Cell

• You might wonder why one doesn't use the formula
  B2C10/C2
• This formula will not fill correctly, since C10
  needs to be used again in each cell (not C11,
  C12, ...)
• This is called freezing C10
• Another correct formula for this cell is
  B2C10/C2, using an absolute cell reference
  for C10 (which can also be done using F4)

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• In fact, electricity costs went down every year
  except one from 1990 to 1998
• In constant 1998 dollars, electricity costs were
  at their highest in 1990, when they were nearly
  10.5 per kilowatt-hour
• The cost dropped every year except 1993
• The minimum was in 1998, at 8.7 per
  kilowatt-hour
• The graph in constant dollars tells a very
  different (and more realistic) story of
  electricity costs.
• In general, most time series in involving money
  should be converted to constant dollars.

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Inflation

• The inflation rate is defined to be the
  percentage increase in the CPI for a given year.
• For example, the CPI in 1997 was 160.5 in 1998
  it was 163.0. The inflation rate for 1998 was
• A graph of the inflation rate over the last
  century tells a very interesting story

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• The inflation rate was positive for all but 12 of
  the 85 years. It peaked in 1918 at 18.0. Its
  minimum was in 1921 at -10.5.
• Inflation was highest overall during World War I
  (1914-1918). (Not coincidentally, the CPI was
  first published in 1919 partly as a response to
  the high inflation of the war years.)
• Inflation was low during the prosperous Twenties
  and was negative during the Great Depression.
• Inflation was high during World War II as well as
  immediately thereafter, reaching a local maximum
  of 14.4 in 1947.
• The Korean War was associated with another
  upspike in inflation, but inflation stayed
  moderate through the Fifties and early Sixties.

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• During the Vietnam War, inflation rose again and
  became a national issue in the early Seventies.
  President Nixon attempted to freeze prices and
  wages with limited success.
• Inflation shot up twice in response to the two
  oil crises (1973-74) and (1979-80), peaking at
  11.0 in 1974 and 13.5 in 1980.
• Inflation moderated during the Eighties but rose
  during the Bush Administration, partly in
  response to the Persian Gulf War.
• Inflation has declined through the Nineties.
• In 1998, it was 1.6, the lowest level in 35
  years (since the early 1960's).
• The last time inflation was negative was 1955.

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Problems with the CPI

• The CPI is widely used as a cost of living index,
  but technically it is not.
• The CPI measures the average change over time in
  the prices paid by urban consumers for a
  relatively fixed market basket of goods and
  services.
• A cost of living index would measure changes over
  time in the amount that consumers need to spend
  to reach a certain utility level or "standard of
  living."
• The CPI completely ignores important changes in
  taxes, health care, water and air quality, crime
  levels, consumer safety, and educational quality.

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• Furthermore, the experience of any individual may
  vary dramatically from what the CPI indicates,
  because an individual's purchasing patterns may
  differ considerably from the standard market
  basket.
• Families with children have considerably
  different buying patterns than elderly
  households, for example.
• The CPI does not even attempt to represent the
  experience of people living in rural areas.

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• For more information on the errors with the CPI,
  see the link for The Consumer Price Index on this
  weeks website