## PRICE, EMPLOYMENT, AND PRODUCTIVITY TERMS AND CONCEPTS

Maintained by: Leigh Tesfatsion
Email: tesfatsi@iastate.edu
Last Updated: 28 March 2015

NOTE: These lecture notes are based in part on materials from R. Hall and J. Taylor (HT), Macroeconomics, W.W. Norton and Company, and from the Economic Report of the President.

## A. THE CONSUMER PRICE INDEX

The consumer price index (CPI) measures the annual cost of living of a typical U.S. urban family. More precisely, the CPI is the current market value of a basket of goods and services deemed to be representative of the type and amount of goods and services purchased by a typical U.S. urban family.

The relative amounts of goods and services included in the basket are determined by a survey of urban consumer buying habits conducted approximately once every ten years. The levels of goods and services included in the basket are normalized so that the value of the basket is \$100 when valued in prices for some conventionally determined base year. The BLS updates the CPI each month by using current prices to re-compute the market value of the CPI basket of goods.

For example, suppose in 2012 that a typical U.S. urban family ate 150 pounds of chicken and 50 pounds of beef, and that the price of chicken in 2012 was \$2 per lb and the price of beef in 2012 was \$3 per lb. Suppose 2000 is the base year, and the price of chicken in 2000 was \$1.00 per lb and the price of beef in 2000 was \$2.00 per lb.

The CPI basket for 2012 is then determined by the following two conditions: It should contain 3 times more chicken than beef (because 150/50 = 3), implying that c = 3b; and the total value of the CPI basket measured in 2000 prices must be \$100, implying that \$1/lb * c lbs + \$2/lb * b lbs = \$100. The amounts c and b of chicken and beef to be included in the CPI basket for 2012 can then be found by solving these two equations for the two unknowns c and b, which gives c = 60 lbs and b = 20 lbs. The CPI for 2012 is then given by the 2012 market value of a basket containing 60 lbs of chicken and 20 lbs of beef, which is \$2*60 + \$3*20 = \$180. The fact that the CPI for 2012 is greater than the base year value of \$100 is interpreted as an indication that the cost of living for a typical U.S. urban family has increased since the base year.

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

An important difficulty with the CPI is that the basket of goods used to represent typical purchases of an urban family is not updated very often and can become outdated. In particular, the relative amounts of goods in the basket 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, U.S. consumers greatly reduced their use of energy in response to increased energy prices. However, the CPI basket in use from 1973 through 1986 was based on a 1973 survey in which energy usage was high, hence it did not reflect this relative drop in energy use. Consequently, the CPI surged upward in these years in response to increased energy prices, greatly exaggerating the actual impact of inflation on a typical U.S. urban family.

## B. DEFINITION AND MEASUREMENT OF THE INFLATION RATE

Given any measure P(T) of the aggregate price level in period T, the corresponding inflation rate from period T to period T+1 is defined to be the percentage rate of change in P(T) from T to T+1, as follows:

```                              P(T+1) - P(T)
(1)         INF(T,T+1)   =   ---------------  *  100%    .
P(T)

```

The GDP implicit price deflator for any period T is defined to be nominal GDP for period T divided by real GDP for period T. By construction, the GDP implicit price deflator reflects prices for all final goods and services newly produced in the economy in period T, hence it is commonly used as a measure for the aggregate price level P(T) in period T. The inflation rate (1) calculated using the GDP implicit price deflator in period T as the aggregate price level P(T) for period T provides a fairly broad measure of inflation as experienced by all purchasers of final goods and services.

Alternatively, economists sometimes calculate the inflation rate (1) using the CPI in period T as the aggregate price level P(T) for period T. In comparison with the inflation rate calculated in terms of the GDP implicit price deflator, the inflation rate calculated in terms of the CPI more narrowly focuses on inflation as experienced by households.

However, the CPI is strongly affected by energy and food costs, which can be extremely volatile. Omitting these more volatile elements from the CPI results in a more stable measure for the inflation rate, referred to as the core rate of inflation, and one commonly sees this core rate of inflation reported in addition to (or even instead of) the CPI measure of inflation.

## C. THE MEASUREMENT OF UNEMPLOYMENT

In order to discuss carefully the appropriate policy responses to unemployment, it is important to understand how unemployment is actually measured in practice. Information on employment in the U.S. comes from two surveys.

(a) A survey of households (Current Population Survey):
The Current Population Survey is conducted each month by the Bureau of the Census, with the data tabulated and reported by the Bureau of Labor Statistics (BLS). The purpose of the survey is to determine how many people of legal age (16 years or older) were employed (paid for at least one hour of work) during the survey week, which is the particular week that includes the 12th day of the month.

(b) A survey of employers:
Employers are surveyed to determine the number of people on the payroll at each place of work. 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 previous four weeks. Given this definition, one can then define practical measures for the labor force, the unemployment rate, and the labor force participation rate as follows:

```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
```

As sensible and straightforward as these measures may seem, they can result in counter-intuitive observations. For example, at the start of an economic expansion, the unemployment rate often rises. How can this be?

By definition, any person who currently is not working and who has stopped seeking work for whatever reason is not counted as part of the labor force. At the start of an economic expansion, many people without jobs who previously had been too discouraged to seek work now begin to seek work and hence are counted as new additions to the labor force. Thus, although the number of employed workers is increasing in absolute terms, the labor force may be increasing at an even faster pace, which results in an increase in the rate of unemployment.

## D. POTENTIAL GDP, THE GDP GAP, AND OKUN'S LAW

To define potential GDP, we first need to clarify what is meant by full employment. We will start with a purely verbal (and somewhat vague) characterization for full employment. Later this will be interpreted in more formal quantitative terms as the level of employment that obtains when the labor market is in equilibrium in the sense that labor demand equals labor supply.

Given any time period T, full employment for period T -- denoted by N*(T) -- is defined to be the amount of employment that would be realized, given existing incentives such as fringe benefits and unemployment insurance, if wages were fully flexible and responsive to demand and supply pressures.

Note, in particular, that N*(T) need not be the maximum amount of employment that the economy is capable of supplying during period T. For example, some people might choose to continue seeking work (to remain unemployed) rather than to accept the jobs that are currently available to them, or they might be in the process of moving from one region to another as part of the employment search process. This type of temporary unemployment is typically referred to as frictional unemployment. Alternatively, some people seeking work might have the wrong skill sets for the available jobs. The latter type of longer-term unemployment is typically referred to as structural unemployment, since it would require some type of retraining (structural changes in skill sets) for such people to find work.

The unemployment rate U*(T) that prevails when employment is equal to full employment N*(T is often called the natural rate of unemployment. Currently in the U.S. the natural rate of unemployment is calculated to be about 6 percent. For reasons that will be clarified in later lectures, the natural rate of unemployment is sometimes also referred to as the "sustainable rate of unemployment" or the "non-accelerating inflation rate of unemployment" (NAIRU).

The level of real GDP that would result in period T if employment were equal to full employment N*(T), denoted by Y*(T), is called the potential GDP for period T. The percentage departure of actual real GDP Y(T) from potential real GDP Y*(T) is called the GDP gap for period T. That is,

```GDP GAP FOR PERIOD T:

Y(T) - Y*(T)
--------------   ,
Y*(T)

where

Y(T)  = actual real GDP for period T ;

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

Empirically, employment is procyclical in the sense that employment moves in step with the business cycle. More precisely, employment is high when actual GDP is high relative to potential GDP and low when actual GDP is low relative to potential GDP.

Given that employment is procyclical, it follows that unemployment is countercyclical -- that is, unemployment is high when actual GDP is low relative to potential GDP (i.e., during times of economic recession) and low when actual GDP is high relative to potential GDP (i.e., during times of economic expansion).

The empirically observed countercyclical nature of the unemployment rate is captured in Okun's Law, expressed as follows: For each percentage point by which the unemployment rate is above the natural unemployment rate, actual GDP is approximately 3 percent below potential GDP.

```ALGEBRAIC FORM OF OKUN'S LAW:

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

|              |
|              |
__  GDP gap __
in period T

where
Y(T)  =  actual real GDP for period T ;

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

U(T)  =  actual rate of unemployment for period T ;

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

E. THE MEASUREMENT OF WAGES AND LABOR PRODUCTIVITY

The hourly nominal wage rate for the U.S. is measured as total labor earnings (dollar value of wages plus fringe benefits) divided by total hours worked. The hourly real wage rate for the U.S. is then measured as the nominal wage rate divided by some measure P for the general price level, generally either the the GDP implicit price deflator or the CPI. In remaining lectures, the following notation will be used:

```  W(T)  =  nominal wage rate during time period T

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

=  Average hourly nominal wage during T

w(T)  =  real wage rate during time period T

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

Productivity is the amount of output produced per unit of input. The most popular measure of productivity, reported by the Bureau of Labor Statistics (BLS), is as follows:

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

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

```