By ANDY ANDREWS
In part one through three of this series, we built a model to calculate expenses, examine testing errors, predict the price of gasoline, “measure” the Consumer Price Index (CPI), and calculate inflation.
While the “silly” model to calculate time entry costs was simple, it made assumptions (e.g., employee quickness) and incorporated facts (e.g., salaries). So did the very complicated CPI. Plus, all of the models include probability and statistics to handle the numbers involved.
Modeling serves many purposes but has two main functions: predicting the future and understanding the process and how it works. Understanding the process and how it works is a backward look at amassed data and determining the relationships among them.
Assume you build a model in physics for which you “think” you know how it works. You make a prediction with the model and run an experiment to collect data. If the data gathered matches the data predicted, you believe your model is an accurate description of the physical process. If it does not match, it is back to exploring the model.
In the CPI model for the United States, data is collected on how 330 million people spend their money annually in a given year. The amassed data are then used to calculate inflation and make adjustments to various values in “running” the government. Then measurement of the CPI begins again. But is the CPI valid for application in small areas of the country or for specific items of consumption? Obviously not is the simple answer but to really assess its value we need to build a personal model.
Per my gathered data, the CPI for last year went up 1.6 percent, was the designated inflation, and affected the compensation I receive from the government. It may not directly affect pay raises awarded by employers, but the data adds (or calculates) up. Concurrently, my county property tax “bill” went up 3.1 percent – more that the CPI’s 1.6 percent. Another example is avocados. Recently they were priced at 88 cents each and in another week the price was three for $5 or 1.9 times (190 percent) higher. This is similar to changes in the price of gasoline as discussed in parts two and three. Values associated with a large group do not necessarily apply to subordinate small groups or individuals.
Let us model a gasoline or diesel engine. In a cylinder of the engine is a mixture of fuel molecules, air molecules, on other “stuff.” When the mixture is compressed and is ignited (or ignites on its own), a chemical reaction occurs. We do not care or track which molecules react with one another. In a two liter, four cylinder engine, each cylinder can contain 1.41 e21 molecules of oxygen, nitrogen, and other stuff. The value “e21” represent 10 raised to the 21st power, a really big number. This is equal to about 4,270,000,000,000 U.S. populations. So we do not care which specific interactions occur. And when we measure things affecting a population of 330 million, we probably do not care about the details of the individual data.
In part two we looked at medical testing and errors in the process. The example used looked for positive and negative results with an error factor. If you assume an error rate of one in every 1,000 tests, be they positive or negative, test everyone in the U.S. for a contagious disease, and that 90 percent of the population is “clean,” 297,000 people who have the disease would be identified a not having is. Yet as an individual, if your test came back as “clean,” your chances of having it would be only one in a thousand. After all, that is based on a “perfect” model.
Compare this medical test to going to the gambling hall and buying a ticket for $1 that has a one in 1,000 chance of winning $1,000. If you win, you will be very happy, you quickly make 1,000 percent on your investment. If you lose, you probably will have very little remorse, it was only a $1. But reverse the game to the blood test where only one person loses, but the loss is your life. This is a very different perspective. Where a small amount of money is at stake, we are not concerned about the losses. But when life is at stake, especially personally, our concern raises exponentially.
In a society, a population has leaders in charge that must make decisions based on “knowledge,” perhaps “models,” that affect and control the population. In the case of the consumer price index we have a model that has evolved over 100 years and has been observed to be very good. While it may be applied to individuals, it affects the entire population in ways we cannot predict, somewhat like fuel molecules in an engine.
But what do you do when something is emerging that can have a major impact on the individual and, perhaps, the entire population? How do you build the model? What are the assumptions? How do you portray the results: individually, collectively as a population, as highly touted specific numbers, or as a percentage? And how do the leadership and policy makers use the values in decision making, policy development, and leadership?
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