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Indexing Data to a Common Starting Point

How 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 X sub tis the raw data value in a given time period from t = 2000, 2001…2013, X sub 0 is the data value in the initial time period, 2000 and X hat sub 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 businesspeople 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.

 

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