In this series of posts [Previous post:GDP Comparisons Across Time], we have demonstrated how apparently objective statistics conceal value judgments. When comparing GDP from one year to the next, we must adjust for inflation. But “inflation” is not a single number – multiple price changes for different goods must be combined into a single measure. This operation is always subjective, and hidden values are concealed within inflation indices, as we will now discuss in greater detail.

Suppose that we ignore both external and internal critique of the concept of GDP as wealth, and accept the idea that wealth in only measured by goods produced in the market, and value of goods can be evaluated at market prices. Even these drastic over-simplifications do not solve our problems, in terms of making comparisons of wealth across time. The problem is the same one that we have discussed earlier. There are multiple goods, and multiple price changes, and we must summarize all the thousands of changes in the quantities of production into one number, and similarly summarize all the prices changes by one number. Because the newspapers report on inflation and on real GDP growth, the public has the impression that this is objectively possible to do. The reality is that there are many different ways to summarize, and every choice among these is necessarily subjective and incorporates value judgments. Let us consider the problem of measuring inflation in greater depth. Note that once we have a measure of the increase in prices, we can automatically divide the nominal growth of GDP in LCU into two parts, one due to price increase, while the remaining growth is due to real GDP growth.

As we have already discussed, there are thousands of goods, and thousands of prices changes. We illustrate the problems which arise in merging multiple indicators into one. Table 3 present as artificial example. Four products are considered in the example. These are wheat, rice, corn and lentils. In year 2000, 300 units of wheat, 100 units of rice, 100 units of corn and 250 units of lentils have been produced. The market prices for these products in year 2000 are 10, 30, 50 and 25, respectively. In 2010, wheat production decreased from 300 units to 100 units and lentils production decreased from 250 units to 60 units. On the other hand, rice production increased from 100 units to 300 units and corn production increased from 100 units to 400 units. The prices of the products changed from 10 to 50, from 30 to 35, from 50 to 40 and from 25 to 75, respectively. Given these prices, Table 3 reports the inflation rates for each product at the last column. They are 400, 16.7, -20 and 200 for wheat, rice, corn and lentils, respectively. In fact, at this point, one could argue that prices are not the same throughout the year. They can fluctuate from day to day or from month to month. So, some sort of averaging is required but this complication is ignored to simplify the discussion.

Table 3: Artificial Example

 Product Quantity (2000) Quantity (2010) Price (2000) Price (2010) Inflation (%) Wheat 300 100 10 50 400 Rice 100 300 30 35 16.7 Corn 100 400 50 40 -20 Lentils 250 60 25 75 200

Now the question is whether the GDP of the country increased or decreased moving from year 2000 to year 2010. Just by looking at the quantities one cannot give the answer. Corn and rice production increased but wheat and lentils production decreased. The standard solution to this problem is to value the products at the market prices. While the value of the year 2000 production with 2000 prices is 17,250, the value of the year 2010 production with 2010 prices is 36,000. So, measured in LCU, the GDP has doubled. The problem is to separate this increase into a price component (inflation) and a quantity component (real GDP). Let us look at how we can try to do this.

We have four rates of inflation, one for each of the four goods – (W: 400%, R: 16.7%, C: -20%, L: 200%). Which of these four factors should be chosen, and what weights should we attach to each factor? This is the standard problem with reducing multiple factors into one. Here we have a very homogenous problem where are four items are food items, which makes it much easier than problems which arise when we are trying to combine an enormous range of diverse goods into one number. But even this extremely simple problem does not have a simple, objective solution, such that all impartial observers would agree on it.  It is generally agreed that the weights which are attached to the four price increases should be the quantities of the goods which were produced. But these quantities also changed from the base year 2000 to 2010. If we use the weights (W:300, R:100, C:100, L:250) from the base year, this is called the Laspayres index, and it come out to 140%. This is because high weights are given to W and L and lower weights to R and C. Since W and L have high inflation rates of 400% and 200%, the weighted average comes out quite high. On the other hand, the Paasche Index takes the weights for the current year, or 2010. The 2010 weights of (W:100, R:300, C:400, L:60) give a lot of weight to the low inflation good R and C which have low inflation rates of 16.7 and -20%. This gives us a Paasche inflation index of only 14%, which is 10 times less than the Laspayres Index of 140%.

Table 4: Analysis of Laspayres and Paasche Index Numbers

 Laspayres Paasche Year 2000 2010 2000 2010 Index 100 240 100 114 Inflation (%) 140 14

Even this very simple example brings the question of which inflation rate should be used. 14% or 140%? There is no answer to this question. But both are “facts”. Going on with the artificial example, we saw the market value of output, which could be GDP, increased from 17,250 to 36,000. That is a 108% increase. If inflation is 14% as calculated by using Paasche index, then there is 94% growth rate. On the other hand, if we use Laspayres index for calculations, then inflation is 140% and growth is -32%. Which figure is correct? There is no answer to this question. To see how this reflects values, suppose that the majority of the public is poor, and eats only wheat and lentils, while a minority is rich and eats rice and corn. Then the Laspayres index better reflects the interests of the poor, who see an average 300% inflation in their food prices. The Paasche index better reflects the interest of the rich, who actually see a decline in their food bills. Every index reflects values which are built into the choices of factors and weights. These choices are arbitrary, and cannot be made objectively. Sensible ways to choose require understanding the goals – WHY are we trying to measure inflation? Without clear thinking about the values involved in constructing the inflation index, and deeper knowledge of the structure of the economy, we cannot find good measures of inflation. However, for most real-world purposes, we will find that multiple measures of inflation would be needed. For example, we could classify the population into quintiles by income, and then consider five different inflation rates, one for each segment of the population. Pragmatically, we cannot consider thousands of numbers at any one time, and for purposes of getting the big picture, it is essential to reduce multiple factors into a small number. However, we must be aware of the distortions which are introduced in this process, and not be deceived by the apparent objectivity of numbers.

(to be continued)

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