## Friday, 7 August 2015

### Inflation Adjustments

When using any variables measured in terms of dollars such as income, earnings, sales, profit, GNP, care must be taken when interpreting changes in these variables over time. To avoid, or more accurately, to correct for the distortion caused by rising prices in a dollar denominated variable, economists construct a new variable known as the real, constant dollar, or inflation-adjusted variable.  In your economics courses you will most likely refer to the variables as real variables, while in any government data sources you will find references to constant dollar variables.
Regardless of what you call it, the concept is straight forward enough.  We want a measure of wages that will indicate no change in wages if both wages and prices double, and a doubling of wages if  wages double and the price level remains unchanged.  To construct such a measure we need to first decide on what measure of prices to use.  In most instances the Consumer Price Index (CPI) is used as a measure for the price level. The CPI, published monthly by the Bureau of Labor Statistics, is simply a weighted average of the prices of goods and services that households purchase.  If you tend to spend considerably more money on food than movies, you will see your cost of living decline more as a result of a 10 percent increase in the price of food than a 10 percent increase in the price of movies.  For a brush up on the CPI you might want to check out a simple example.
Once you have the price data, the procedure for adjusting the nominal quantity is quite simple, but extremely useful.  In the following example nominal (actual) wage data is corrected to create real (inflation adjusted) wage data. The formula for the adjustment is:
R = N/PI *100
R = real value (constant dollar)
N = nominal value (current dollar)
PI = price index
And the adjustment does matter. To see how much, check out the analysis of the financial situation at URI.  Here we will return to our Slippery Slope example to examine the impact of the adjustment.  To incorporate into the analysis any effect of price inflation, we must start with getting information on the price level. In the third column  information on the price level has been added.  The Price Index column is the Consumer Price Index (CPI) that you hear people talk about every month and that you can get directly from the Bureau of Labor Statistics site or from the Economic Report of the President tables
 Revenue Price Index 1991 100 136.0 1992 90 140.3 1993 92 144.5 1994 95 148.2 1995 98 152.4 1996 101 156.95
With these data, and using the formula above, we can create a new concept called 'inflation adjusted', or Real Revenues. The 'real' data appear in the last column in the table below. What we see is that during this time Real Revenue actually declined by nearly 13 percent (64.30 - 73.53)/73.53.  The problem is , the real revenue figures are not numbers that are easy to explain.  This difficulty can be traced to the fact the price index has a base year (when the price index is 100) outside of the sample range so all of the numbers are specified in terms of that year.   What you can say based on these numbers is real wages have fallen 13 percent, you just can't say much about the actual numbers.
 Revenue Price Index Real Revenue 1991 100 136 73.53 1992 90 140.3 64.15 1993 92 144.5 63.67 1994 95 148.2 64.10 1995 98 152.4 64.30 1996 101 156.95 64.35
This problem can be remedied if we convert all of the numbers based on one of the years in the sample.  Two obvious choices would be the beginning or the ending period. My suggestion would be to express the numbers in terms of the year closest to the one that you are in.  In this case, your analysis would be best if you expressed things in terms of 1996.  To obtain these numbers all that you need to do is modify the formula specified above.  The formula to get a column of real data in 1996 prices would be:
R(96) = [N/PI]*PI(96)
The term in brackets [N/PI] is the original measure of real wages and this is multiplied by the price index in 1999 PI(96).  You need to use the formula for real and then multiply the entire column by the price level in 1996 [PI(96)].  You know you have done it correctly if the nominal and real values for 1996 are the same.  The results appear in the table below.
 Revenue Price Index Real Revenue 1991 100 136.0 115.4 1992 90 140.3 100.7 1993 92 144.5 99.9 1994 95 148.2 100.6 1995 98 152.4 100.9 1996 101 156.95 101.0
What we see here is real revenue in 1996 was virtually unchanged from what it had been in 1992, and substantially lower than 1991.  In fact you will see the decline in real revenue is the same when measure in terms of percent [(101-115.4)/115.4 = (64.30 - 73.53)/73.53].  The difference is that the 1996 numbers are easier to explain.  In 1996 revenue at the university was 101, down approximately 13 percent from 115.4 in 1991.  If you want more information on this you should work through a second example.
The importance of the adjustment is also evident in the two graphs below entitled Average Weekly Earnings.  In the top graph, the untrained eye sees continual improvement in average weekly earnings. From an average of roughly \$80 a week in 1960, weekly earnings rose to \$370 in 1993. Furthermore, given the fact that earnings increased at an average yearly rate of 4 percent in both the 1960s and 1980s, and 7 percent in the 1970s, one might be led to believe the 1970s was a period of more rapid growth, an observation that repeatedly appears in students' initial reports on economic growth in the post WW II period.
Anyone aware of that period knows this is not an accurate portrayal, a fact more than adequately reflected in the second Weekly Earnings graph in which you find the data for wages adjusted for inflation. Real earnings of American workers peaked in 1973 and by 1990 they had fallen to 1960 levels. Yes wages increased 7 percent per year in the 1970s, but prices increased nearly 8% giving us an average yearly 'decline' of 1% in wages.
This diagram also helps explain the proliferation of reports indicating the plight of Generation X, those who are moving into the labor force in the early 1990's. The forecasts that this generation may be the first to not achieve a standard of living higher than that of their parents is simply the result of an extrapolation of existing trends.

A similar problem exists when we examine interest rates or other rate of return variables. Consider the position of a money lender who must determine the appropriate interest rate to charge. Certainly one of the considerations will be the rate of inflation, the rate of increase in the price level (CPI). If the inflation rate is 6 percent, a lender must receive 6 percent interest just to maintain the money's buying power.  Stated somewhat differently, if the cost of living increases 6 percent this year, then what you can buy this year for \$100 will cost \$106 next year. In this situation a lender must charge 6 percent to stay even - so as to receive the \$106 in one year. If on the other hand, the lender wanted a 2 percent return on money, then the interest rate would need to be 8 percent  with 6 percent simply accounting for inflation.
The realization that inflation rates are a common denominator in interest rates has prompted economists to develop a concept called 'real interest rates'.  The unobserved 'real' rate which is what 'really' matters to decision makers, is defined as the actual rates minus the expected inflation rate. The relationships between real and nominal rates is captured in the equations where the expected inflation rate equals the actual rate:
rr = rn - i
where:
rn = actual interest rate (what you see in the news)
rr = real interest rate i = inflation rate
As with wage earnings, there is a significant difference between the movement in real and nominal interest rates. In the 1980s for example, nominal short term rates on government securities fell sharply from 11.5 percent in 1980 to 6 percent in 1986 before rising to 7.5 percent in 1990. Real interest rates, meanwhile, moved in the opposite direction. After actually being negative in 1980, real rates rose to 4.1 percent in 1986 and then fell back towards 2 percent in 1990.

The bottom line is that inflation matters and that financial data, numbers expressed in dollar quantities, need to be adjusted for changes in the price level.  Now we will move on to a discussion of benchmarking, adjustments for scale differences.

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