Data concepts

 

Principles and risks of forecasting (pdf)

Famous forecasting quotes
How to move data around
Get to know your data
Inflation adjustment (deflation)
Seasonal adjustment
Stationarity and differencing
The logarithm transformation

 

Inflation adjustment


Inflation adjustment, or "deflation", is accomplished by dividing a monetary time series by a price index, such as the Consumer Price Index (CPI). The deflated series is then said to be measured in "constant dollars," whereas the original series was measured in "nominal dollars" or "current dollars." Inflation is often a significant component of apparent growth in any series measured in dollars (or yen, euros, pesos, etc.). By adjusting for inflation, you uncover the real growth, if any.  You also may stabilize the variance of random or seasonal fluctuations and/or highlight cyclical patterns in the data.  Inflation-adjustment is not always necessary when dealing with monetary variables--sometimes it is simpler to forecast the data in nominal terms or to use a logarithm transformation for stabilizing the variance--but it is an important tool in the toolkit for analyzing economic data.

The Consumer Price Index is probably the best known US price index, but other price indices may be appropriate for some data. The Producer Price Index and the GDP Implicit Price Deflator are some other commonly used indices, and numerous industry-specific indices are also available.  The U.S. Bureau of Economic Analysis compiles a wide array if "chain-type" price indices for various kinds of personal consumption goods.  A chain-type index is one that is obtained by chaining together monthly, quarterly, or annual changes in relative prices that are adjusted for changes in the composition of the commodity basket, so as to reflect changes in consumer tastes.  (For more details on chain-type indices, see the following article.) 

The following chart shows price indices for a variety of products and services over the period from 1997 to 2010, all scaled to a value of 100% in 1997.   There are some striking differences:   the price of gasoline has experienced large downward as well as upward movements due to shocks to the world economy, tobacco prices have risen in large part due to taxation, the price of a college education has gone up dramatically in stair-step fashion, and the price of computers has shown an exponential decline rather than exponential growth.  (The ordering of the series in the legend is the same as their rankings in 2010, except that the all-items index should be ranked below rather than above fast food.)

Use of an appropriate price index is important if you are interested in knowing the true magnitudes of trends in real terms and/or if the relevant price history has undergone sudden jumps or significant changes in trend rather than consistent increases over time.   However, deflation by a general-purpose index such as the CPI is often adequate for rough estimates of trends in real terms when doing exploratory data analysis or when fitting a forecasting model that adapts to changing trends anyway.  Keep in mind that when you deflate a sales or consumer expenditures series by a general index such as the CPI, you are not necessarily converting from dollars spent to units sold or consumed, rather, you are converting from dollars spent on one type of good to equivalent quantities of other consumer goods (e.g., hamburgers and hot dogs) that could have been purchased with the same money.  Sometimes this is of interest in its own right because it reveals growth in relative terms, compared to prices of other goods.

Here is a graph of the auto sales in nominal dollars plotted alongside the CPI for the 25 years from 1970 to 1995, where the CPI has been scaled so that the January 1990 value is 1.0.

Now here is a graph of auto sales divided by (i.e. deflated by) the CPI. Note that much (though not all) of the upward trend has been removed, accentuating the seasonal and cyclical components of the data. The recessionary periods in the mid-1970's, early 1980's, and early 1990's are especially evident:


To perform the inflation adjustment in Statgraphics, you merely have to type the expression AUTOSALE/CPI as the input variable (assuming that AUTOSALE and CPI are pre-existing variables). If you wanted to perform the same calculation on a spreadsheet, it would look like this:


When looking at descriptions of time series obtained from government or commercial data sources, the identifier "$" or "dollars" means the series is in nominal dollars (i.e., not inflation-adjusted). An identifier such as "1990 dollars" or "1990 $" means that the series is in constant (inflation-adjusted) dollars, with 1990 taken as the reference point. For modeling purposes, the choice of a reference point doesn't matter, since changing the reference point merely multiplies or divides the whole series by a constant. To move the reference point to a different base year, you would just divide the whole price index series by the current value of the index at the desired reference date. However, the parameters of a model are easier to interpret if the same reference point is used for all inflation adjustments. The thing you wish to avoid at all costs is having some variables which are inflation adjusted and others which aren't: this will introduce apparent nonlinear relationships which are merely artifacts of inconsistent units.

The following spreadsheet illustrates how you could adjust the auto sales series to 1970 dollars instead of 1990 dollars. First, the CPI series is divided through by its original value in January 1970, to obtain a new consumer price index series called CPI70 in which the 1970 value is equal to 1.0. Then the auto sales series is divided by the CPI70 index:

Of course, the graph of the auto sales series in 1970 dollars would look identical to the graph in 1990 dollars: only the axis scale numbers would change.


Finally, remember that inflation adjustment is only appropriate for series which are measured in units of money: if the series is measured in number of widgets produced or hamburgers served or percent interest, it makes no sense to deflate. If a non-monetary series nonetheless shows signs of exponential growth or increasing variance, it may be useful to try a logarithm transformation instead.

Go on to next topic:  Seasonal adjustment