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Indexing Data to a Common Starting Point

iconHow to index any economic data series to a common starting point to facilitate the comparison of numeric data.

The Economic Problem

Indexing Is Kind of Like a Race

That a racehorse can run is relatively uninteresting. Of more intrigue to bookies and bettors is that a given racehorse can run relatively faster than another. Few would come to watch randomly placed horses gallop around a track, each starting and stopping at will and each with its own finish line. It’s the comparison of competing horses and subsequent ranking that make a race compelling.

To create a fair comparison, track officials normalize the beginning point with a start gate, release all horses at the same time and use precision measuring instruments to determine a winner. Clearly, some racehorses are faster and stronger than others. But without a common starting point, any determination of physical supremacy would be dubious.

A similar case holds true with economic data. Economists like to compare data. They do so to gain perspective and to put things in context. For instance, knowing that a state’s employment is growing over time is useful. But knowing its growth rate relative to other states is more telling. For example, a state’s rate of employment change, though positive, could be the weakest of the 50 states in a sample.

Start Data at the Same Point

A relatively simple way to make such comparisons is by indexing data to a common starting point. In effect, the variables in question must be set equal to each other and then examined over time for differences. Indexed data are handy because they allow an observer to quickly determine rates of growth by looking at a chart's vertical axis. They also allow for comparison of variables with different magnitudes.

Indexing Enables Comparison of Data of Any Magnitude

For example, suppose an analyst wants to use a graph to compare the gross domestic product (GDP) of three different countries. Drawing such a chart with absolute values would be difficult because of the size disparity between countries. One country’s GDP might register in the trillions, another in the hundreds of billions and the other in the tens of billions. All these amounts wouldn’t fit well on the chart.

As another example, Chart 1 shows how dissimilar magnitudes in quarterly employment levels in Texas and the United States make for difficult graphical interpretation. This chart demonstrates that the level of employment in the US is substantially larger than employment in Texas, but because of this large disparity in magnitude, it's impossible to tell from this chart whether employment in Texas rose (or declined) faster or slower than employment in the U.S. from 2003 to 2012.

Indexing numerical data is useful in a variety of contexts. It shows up all the time in economic, financial and business analysis. Equity traders index stock prices and stock indices to compare performance over time. Economists index data to prominent events—say economic peaks (or troughs)—to see how the data decline (or rise) relative to each other. In all cases, it allows for quick comparison and ranking.

The Technical Solution

Indexing Mechanics

To index numerical data, values must be adjusted so they are equal to each other in a given starting time period. By convention, this value is usually 100. From there on, every value is normalized to the start value, maintaining the same percentage changes as in the nonindexed series. Subsequent values are calculated so that percent changes in the indexed series are the same as in the nonindexed.

Consider the data in Table 1. Variables X and Y represent hypothetical data series. On average variable Y is one order of magnitude larger than variable X. To index the two series, apply the following equation to the raw data:

X hat sub t equals the ratio of x sub t and x sub 0 multiplied by 100

Where Xt is the raw data value in a given time period from t = 2000, 2001…2013, X0 is the data value in the initial time period, 2000 and X^t is the new indexed value of the variable.

Table 1
Indexing Two Data Series
Year X Y Indexed value of
X
Indexed value of
Y
2000 250 2000 100 100
2001 500 3000 200 150
2002 810 6000 324 300
2003 925 6500 370 325
2004 1010 6500 404 325
2005 1052 7100 421 355
2006 1030 7300 412 365
2007 1240 7600 496 380
2008 1470 7800 588 390
2009 1500 8300 600 415
2010 1525 9200 610 460
2011 1580 9900 632 495
2012 1740 10,200 696 510
2013 1890 9800 756 490

Between 2000 and 2001, variable X increased from 250 to 500, or 100 percent. Consequently, the indexed value of X must also increase 100 percent, from 100 to 200. Similarly, Y increased 50 percent between 2000 and 2001. Thus the indexed value of Y increased 50 percent, from 100 to 150, over the same time period.

Indexing allows you to quickly gauge percentage changes between the initial time period and any subsequent time period. For example, between 2000 and 2013, variables X and Y increased 656 and 390 percent, respectively.

Real-World Example

Applying the Technique to Texas and U.S. Employment

Indexing improves the ability to analyze changes in data over a specified time period. In the example of the U.S. and Texas employment levels, it was difficult to see how job growth in Texas compared with job growth at the national level. However, such a comparison is possible with indexed data.

The Calculations

In Table 2, each value in the U.S. column is divided by 130,093 and multiplied by 100 to arrive at an indexed value. Likewise, each value in the Texas column is divided by 9,394 and multiplied by 100.

Table 2
Indexing Texas and U.S. Employment Data
Period U.S. Texas U.S. indexed Texas indexed
2003 - Q1 130,093 9,394 100.0 100.0
2003 - Q2 129,843 9,368 99.8 99.7
2003 - Q3 129,871 9,345 99.8 99.5
2003 - Q4 130,175 9,375 100.1 99.8
2004 - Q1 130,563 9,419 100.4 100.3
2004 - Q2 131,285 9,460 100.9 100.7
2004 - Q3 131,623 9,501 101.2 101.1
2004 - Q4 132,206 9,564 101.6 101.8
2005 - Q1 132,660 9,605 102.0 102.2
2005 - Q2 133,388 9,679 102.5 103.0
2005 - Q3 134,132 9,764 103.1 103.9
2005 - Q4 134,596 9,823 103.5 104.6
2006 - Q1 135,402 9,924 104.1 105.6
2006 - Q2 135,912 9,998 104.5 106.4
2006 - Q3 136,350 10,058 104.8 107.1
2006 - Q4 136,700 10,151 105.1 108.1
2007 - Q1 137,243 10,232 105.5 108.9
2007 - Q2 137,591 10,335 105.8 110.0
2007 - Q3 137,659 10,415 105.8 110.9
2007 - Q4 137,885 10,483 106.0 111.6
2008 - Q1 137,935 10,562 106.0 112.4
2008 - Q2 137,443 10,607 105.6 112.9
2008 - Q3 136,711 10,635 105.1 113.2
2008 - Q4 135,087 10,618 103.8 113.0
2009 - Q1 132,812 10,516 102.1 111.9
2009 - Q2 130,945 10,330 100.7 110.0
2009 - Q3 129,944 10,248 99.9 109.1
2009 - Q4 129,447 10,213 99.5 108.7
2010 - Q1 129,319 10,229 99.4 108.9
2010 - Q2 129,960 10,290 99.9 109.5
2010 - Q3 129,920 10,346 99.9 110.1
2010 - Q4 130,226 10,408 100.1 110.8
2011 - Q1 130,685 10,452 100.5 111.3
2011 - Q2 131,237 10,530 100.9 112.1
2011 - Q3 131,531 10,582 101.1 112.6
2011 - Q4 131,985 10,606 101.5 112.9
2012 - Q1 132,681 10,711 102.0 114.0
2012 - Q2 133,004 10,757 102.2 114.5
2012 - Q3 133,416 10,808 102.6 115.0
2012 - Q4 133,864 10,875 102.9 115.8

Texas Grew Faster than the U.S. over the Study Period

Chart 2 illustrates the effect of indexing the two data series. From 2003 to 2008, employment in Texas grew at a much faster rate than national employment. In addition, since the most recent recession, Texas employment growth has continued to outpace the rest of the U.S.

Summary

The indexing methodology can be used with various types of economic data. It can be an effective means of normalizing data to a common starting point and observing how variables change over time relative to each other. It is a common method used by economists and business people to enhance perspective and understanding of economic trends.

Glossary at a Glance
Indexing:
Modifying two or more numeric data series so that the resulting series start at the same value and change at the same rate as the unmodified series.
DataBasics