Advanced Lecture Notes for Hall and Taylor, Chapter 3

MEASURING THE COST OF LIVING AND INFLATION

Basic References: Macro Principles Review;
                  HT Chapter 3; Study Guide, Chapter 3

A. THE CONSUMER PRICE INDEX (CPI)

     The #consumer price index# (CPI) measures the annual cost
of living of a typical urban family in the U.S.  A basket of
goods and services is determined by the Bureau of Labor
Statistics (BLS) to reflect the buying habits of typical urban
consumers.  This basket of goods and services contains both
domestically produced and foreign-produced goods and services.

     The #relative# amounts of goods and services included in
the basket are determined on the basis of urban consumer buying
habits [based on a survey conducted approximately once every ten
years].  The #levels# of goods and services included in the
basket are scaled so that the value of the basket measured in
prices for some "base year" is $100.  Note that Hall and Taylor
(Fourth Edition) use 1987 as the base year for the CPI.

     Each month the BLS updates the CPI by using detailed
current prices to re-compute the cost of the CPI basket of
goods.

#Example#:

     Suppose in 1990 that urban consumers on average ate three
times as much chicken c as beef b (measured in lbs).  In the
base year 1987 the price of chicken was $1.00/lb and the price
of beef was $2.00/lb.  The basket q = (c,b) for the "CPI" in
1990 is then determined by the two conditions

  c  =  3b     and      [$1.00 ] x c  + [$2.00] x b  =  $100 ,

which yields

     [$1.00] x 3b  +  [$2.00] x b  =  $100

or
       5b  =  100

or

       b = 20    and    c = 3b = 60.

It follows that the "CPI" for 1990 is given by the dollar value
of the basket q = (c,b) = (60,20) #in 1990 prices# for chicken
and beef:

     CPI(1990)  =   P`c(1990) x [60]  +  P`b(1990) x [20]   .

If this amount is greater than $100.00, one can conclude that
the "general price level" has increased.

     In the U.S., the CPI is the most widely used measure of the
purchasing power of U.S. currency (the dollar).  For example,
wage contracts which contain cost-of-living-adjustment (COLA)
provisions to protect workers against price increases require
wages to increase in proportion to increases in the CPI.  Social
security benefits are also now indexed to the CPI or a wage
index, whichever is lower.

     A difficulty with the CPI is that the expenditure weights
(basket of goods) used to represent typical purchases of an
urban family is not updated very often, and can become outdated.
In particular, the expenditure weights are not varied in
response to price changes, even though consumer purchases may be
highly elastic with respect to price changes.

     For example, after the 1974 oil price shock people greatly
reduced their use of energy.  Nevertheless,the CPI expenditure
weights used through 1986 were based on a 1973 survey and hence
did not reflect this reduced usage.  Consequently, the upward
surge in the CPI during these years in response to increased
energy prices greatly exaggerated the actual rate of inflation
faced by a typical urban family.  For example, in 1980 the CPI
indicated a 17% inflation rate whereas the implicit price
deflator for the consumption component of GNP indicated only a
12% inflation rate.  The 17% rate created a panic in the Carter
administration, leading to the introduction of credit controls
and other dubious measures.

[R. J. Gordon, "The Consumer Price Index: Measuring Inflation
and Causing It," #The Public Interest# 63 (Spring 1981),
112-134]


B.  THE PRODUCER PRICE INDEX (PPI):

     The #producer (formerly, wholesale) price index# measures
the prices paid by producers at various stages in the production
process for crude materials and intermediate goods.  There is no
clear basis for the choice of the weights for the PPI.


C.  PRICE DEFLATORS FOR GDP AND ITS COMPONENTS

     Previously we defined the GDP Implicit Price Deflator P(T)
associated with the GDP for some specified year T to be [Nominal
GDP]/[Real GDP], where "nominal" GDP for year T is GDP for year
T valued in current year T prices and "real" GDP for year T is
year T GDP valued in base year (1982) prices.  A price deflator
can also be associated with each #component# of GDP.  For
example, the "consumption deflator" for year T is defined by

              [nominal year T consumption spending]
 P`C(T)   =   -------------------------------------   ,
                [real year T consumption spending]

and similarly for investment, government expenditures, and net
exports.

     Since GDP does not include imports and consumption C does,
the GDP implicit price deflator will differ from the consumption
deflator in years when there are large shocks to import prices.


D. MEASURING INFLATION

     The #rate of inflation (deflation)# is the percentage rate
of increase (decrease) in some specified price index over some
specified interval of time.

#Examples#:

     The rate of Inflation over any time interval T to T+1
measured in terms of the implicit GDP price deflator P(T) is
given by

                         P(T+1) - P(T)
     c^{GNP}(T,T+1)  =  ---------------      ;
                              P(T)


and the rate of inflation over any time interval T to T+1
measured in terms of the consumer price index CPI(T) is given by


                         CPI(T+1)  -  CPI(T)
     c^{CPI}(T,T+1)  =  ---------------------    .
                                CPI(T)



            #MEASURING EMPLOYMENT, UNEMPLOYMENT, AND WAGES#

Information on employment in the U.S. comes from two surveys:

     (a) A survey of #households#  (The "Current Population
Survey") conducted each month by the Bureau of the Census, with
the data tabulated and reported by the BLS, to find out how many
people of legal age (16 years or older in the U.S.) were
employed (paid for at least one hour of work) during the "survey
week," i.e., the week that includes the 12th day of the month.

    (b) A survey of #employers# to find out the number of people
on the payroll at each workplace.  The survey excludes farm
employees and the self-employed.

The Current Population Survey undertaken in a particular month M
counts a person as #unemployed for month M# if that person did not
work either full-time or part-time during the survey week for month M
but did look for work during the past four weeks.

 Labor Force for month M  = Number of legal-aged persons who were
  (U.S. definition)         either working or unemployed during month
                            M according to the Current Population Survey.

                         Number of Unemployed Workers During Month M
 Unemployment Rate  =   ---------------------------------------------
 for month M                   Labor Force During Month M


                                     Labor Force During Month M
 Labor Force Participation   =   ------------------------------------
 Rate for Month M                Working Age Population During Month M


#NOTE#:  Calculations of these concepts for (e.g.) quarterly or
year-long time periods can be calculated as appropriate averages of
monthly rates.


Define N*(T) =  potential employment for time period T

             =  amount of employment which would obtain in
                period T, given existing incentives such as
                fringe benefits and unemployment insurance,
                etc., if real wages were fully flexible and
                responsive to demand and supply pressures.

Note that N*(T) is not the maximum amount of employment that the
labor force is #capable# of supplying during time period T,
because some members of the work force may choose to search for
a better job, or to undergo job training, rather than to accept
a job that has been offered to them.  This type of unemployment
is called "frictional" or "voluntary" unemployment.

     The unemployment rate which prevails when employment is
equal to potential employment N*(T) is called #the natural rate of
unemployment#, denoted by U*(T), and represents frictional
unemployment.  Currently in the U.S. the natural rate of
unemployment is calculated to be about 6 percent.

     The level of real GDP which would result for time period T
if employment were equal to potential employment is called
#potential real GDP#, or alternatively #the full employment
level of output#, and will be denoted by Y*(T):

      Y*(T)  =  potential real GDP for time period T

             =  real GDP for time period T which would result if
                employment were equal to potential employment N*.

The percentage departure of real GDP from potential real GDP is
called the #GDP gap#.

      GDP gap for period T  =  [Y(T) - Y*(T)]/Y*(T)  .

     Employment is #procyclical# in the sense that employment
moves in step with the business cycle.  More precisely,
employment is high when real GDP is high relative to potential
real GDP, and vice versa.  Conversely, #unemployment# moves in
#countercyclical# fashion--high in recessions and low in
boomtimes.  This latter empirical regularity is captured in
#Okun's Law#, which says that for each percentage point by which
the unemployment rate is #above# the natural rate, real GDP is 3
percent #below# potential GDP.


ALGEBRAIC FORM OF OKUN'S LAW:

     [Y(T)  -  Y*(T)]/Y*(T)    =    - 3 x [U(T) - U*(T)]  ,

       |              |
       |              |
        __  GDP gap __
         in period T
where

          Y(T)  =  real GDP for period T

          Y*(T) =  potential real GDP for period T

          U(T)  =  rate of unemployment for period T

          U*(T) =  natural rate of unemployment for time period T


     Wages and prices generally moved together throughout the
swings in inflation in the 1970's.  The nominal wage is
generally measured by total labor earnings (dollar value of
wages plus fringe benefits) divided by total hours worked.  The
#real wage# is the nominal wage divided by the cost of living as
measured by the CPI or some other general price index, say P.


  W(T)  =  nominal wage during time T

             Total labor earnings during T
        =  ------------------------------------
           Total number of hours worked during T

        =  Average hourly wage during T.



  w(T)  =  real wage during time T

             W(T)
        =  -------
             P(T)


     Productivity is the amount of output produced per unit of
input.  The most popular measure of productivity, put out by the
BLS, is:

  Labor Productivity   =  Average output per hour of labor during T
  During Period T

                       =  Real GDP originating in the business sector
                          during T divided by the total hours of work
                          in the business sector during T

Productivity growth in the U.S. has been disappointing since
1973, below the normal trendline growth rate.  This slowdown in
productivity is an ongoing puzzle.