Scale Adjustments: Bench marking

Let's assume we are interested the performance of Rhode Island's economy. In the decade ending in 1993, wage and salary income in the State increased 75 percent, employment increased 4 percent, and the average price of a home in Providence rose over 100 percent. That, and 25 cents, might get you a phone call. There is no benchmark against which to evaluate these numbers.  A 4 percent employment increase sounds low, but what if employment elsewhere were actually falling? On the other hand, the 75 percent increase in wage and salary income sounds impressive, but what if the average for the other 49 states was 120 percent?

To avoid being misled by the absolute numbers, in this section we will look at two 'bench marking' techniques that will be used to provide some cross-section perspective.  The example will be construction employment in RI and the US for the period 1983-1993.

Construction Employment (1,000s)

The first bench marking technique is particularly useful when comparing two variables that are of very different orders of magnitude - precisely the problem when analyzing the performance of employment in Rhode Island relative to that in the US. The problem with the employment data is it is impossible to construct a meaningful graph of Rhode Island and the US employment because of the large difference in scales. The line for construction employment in RI appears as a straight line near the axis because the scale is set to accommodate the numbers for the US, that are in millions, while the numbers for RI are in thousands.

The differences between the performance of the construction employment in RI and the US can be better represented by the creation of index numbers that provide us with a second solution to the problem of analyzing these data. The advantage of the index approach is it provides a better visual representation of comparative growth, while its disadvantage is the index number is not readily understood by the lay reader without some guidance. The index numbers are constructed by taking all the numbers in a column and dividing them by the first number.

Construction Employment Indexes

In the US column for example, each of the numbers is divided by 3,877, while for RI each number was divided by 9.9. As you can see, all the columns of indexes begin at 1 which is what you would expect since you are dividing a number by itself. For the other years you should interpret the index numbers as giving you a measure of the changes in construction employment over a specific period of time.

The results of applying this index approach to employment in construction are dramatic.  For example, the 1.33 figure for the US in 1989 tells us that between 1983 and 1988, employment in the US has increased by 33 percent.  During the same time period construction employment in RI increased 83 percent, evidence of the speculative nature of RI's construction boom in the mid 1980s that laid the groundwork for the collapse in the late 1980s.

A second approach to bench marking RI's performance would be to look at the State's relative performance. One of the most common measures of relative performance would be a ratio. In the table above, the figures in the last column were derived by dividing RI employment into the US total for the same year. For example, the .35% figure for RI in 1989 equals 17/4969*100.

Rhode Island's Relative Employment

How do we interpret the table of ratios? One must be quite careful. The ratio form allows us to look at how the state has performed relative to the nation, but we lose information about the actual performance of the state when we construct the ratio. It is impossible to tell what happened in RI from looking at only the ratio.  Stated somewhat differently, a decline in the RI/US ratio could happen in each of the following cases:

1. employment rises slower in RI than the US
2. employment falls faster in RI than the US
3. employment falls in RI and rises in the US
4. employment falls in RI and remains unchanged in the US
5. employment remains unchanged in RI and rises in the US

The advantages of the relative variable can also be seen in the graphs for wages in RI. In the graph of RI's wages, there is every indication that wages were increasing throughout the post W.W.II period.  A very different picture emerges, however, when we look at the graph of the ratio of RI to US wages. In the period 1950 to 1978, RI's wages fell from approximately 88 percent of the US average to approximately 73 percent of the US average. During this period wages in RI grew, but more slowly than they did in the US. This trend was reversed in the 1980s as wages in RI began to rise faster than wages in the rest of the nation. Unfortunately for those of you who are Rhode Islanders, the long term pattern of decline had been reestablished by the early 1990's.

Before we leave this section, let us ask the questions: What would employment in RI have been in 1989 if it had grown at the same rate as the US, and what would employment in RI have been in 1989 if its share of national employment had remained unchanged?  The fact is that they are the same question.  If employment grew at the same rate in RI and the US, then the share would have remained constant.  In answering one of the questions we are answering both. 

Let's approach it from the constant share side. RI construction employment in 1989 was 18,200 which represented .35 percent of the nation's total construction employment. This was an increase of .09 percentage points from the 1983 share which explained RI's faster than average growth.  By 1989 employment in RI had increased 83.8 percent, substantially more than the 33.5 percent increase nationally.  If the share had remained the same (.26 percent), then RI employment in 1989 would be .26 percent of the national total which is 13,455 [.0026*5175]. Stated somewhat differently, RI's above average growth was responsible for 4,745 jobs in the construction industry - jobs that could not be explained by the national growth. You will end up in the same place if you let employment in the state grow at 33.5 percent.

For a second example of scale adjustments, let's return to one our opening question-the renewal decision at Slippery Slope. To evaluate the President, the decision has been made to consider the revenues situation at other comparable universities during this time period. The table below has the revenue figures for Slippery Slope and the entire sample of comparable universities.

Slippery Slope University Revenues

With this new information, what can we say about the President's relative performance? There are two techniques that we might use to answer this question. One would be to look at the ratio of Slippery Slope to the revenue for the entire group of universities. If we adopt the President's view that we should begin in 1992, he has been successful at increasing Slippery Slope's share of total revenue from 6.9 to 7.5 percent because revenue has increased faster at Slippery Slope (12 percent) than for the entire group (3 percent).

Slippery Slope University Revenues

For those who like visuals, here is what the graph of Slippery Slopes's relative performance. Given that we are graphing a ratio (SS/Total), when this graph slopes downward it means that Slippery Slope is not doing as well as the total and when it has a positive slope, Slippery Slope's revenue is growing faster than the total.

Another way to look at it would be with the use of an index number. Below you will see a table containing the original figures plus the new indexes for Slippery Slope and the Total. The indexes were constructed by dividing each of the original columns by the corresponding 1992 figure.

Slippery Slope University Revenues

Based on these data we know that Revenue at Slippery Slope increased 12 percent [we take away 1 from the index 1.12 and have .12 which equals 12 percent] while revenue for the entire group of universities increased 3 percent [we take away 1 from the index 1.03 and have .03 which equals 3 percent]. The graphical representation of these two are presented below.

What's the verdict? As I indicated at the outset, this was not going to be easy. The bad news for the President is that revenues have gone up, but not after we account for inflation. The university is about where it was in 1992 in terms of the buying power of its revenue. The good news is the President's university seems to have done better than the other universities. The review is mixed, and the decision will be a difficult one, but I hope that you can see how a little data analysis can go a long way toward helping us make a more informed decision.