Price Indexes (13) Shooting the Messenger

Some economists are pretty hard on statisticians. They see them as a government tool for manipulating the masses. This statement is a little unfair. Most of the statisticians that I know are very independent thinkers determined to measure the economy accurately. Most have an obsession with detail and a fixation with doing things accurately (other personality types find the work boring). They put enormous effort into producing correct estimates.

Statisticians actually have a prophetic role. They are often the only ones who can expose the full impact of government’s monetary policies. The central bankers are the ones who inflate and devalue the currency. I suggest that we concentrate on getting rid of them, rather than attacking those who measure the damage they do. Until we have sound money and inflation disappears, we will need statisticians to measure the impact of monetary manipulation.

I agree that a government monopoly is wrong and dangerous. The best way to get reliable statistics would be to have various providers competing in an open market for statistics. This is what economists should be arguing for, rather than undermining the practice of statistics.

Developing measures that are as accurate as possible is not easy, and there will always be debate about methods. Statistical journals are full of debates about the merits and problems of different methods, including hedonic adjustment. Rather than complaining about the work of statisticians, economist should be glad that they are exposing the damage done by monetary inflation.

Another good example of the prophetic role of the statistics profession is the manual for Government Financial Statistics. This is a system developed by statisticians for measure government income and expenditure. This system exposes the multitude of sins that are hidden by the cash based accounts kept by most modern governments. If all governments adopted these standards, there economic management would be much more transparent.

To those looking for a conspiracy, I am sorry guys, but I don’t think it is there. You should about be careful about the way you use statistics, and make sure that you understand what they measure, but encouraging conspiracy theories adds more heat than light. Statistics and statisticians actually expose the consequences of politician’s actions.

Price Indexes (12) Statistical Monopoly

One reason for the concern about the validity of price inedexes is that we do not have a free market for statistics. Monopoly governments have crowded out most private operators, so users have very little choice.

If the government stopped producing statistics, there might be a market for privately produced statistics. If inflation of the money supply continued, I suspect that there would still be a demand for price indexes and measures of GDP estimated by private suppliers.

Private production would be preferable, as any incentive to cheat would be removed. However, we would still need independent private experts to monitor the work of the private statisticians to assess the quality of their work.

Price Indexes (11) Deflating Output Measures

Economists are often concerned about the impact that quality adjustment or hedonic adjustment might have on the measurement of real GDP. Given a certain nominal GDP (in dollars or any other currency unit), the number for the price deflator determines the size of real GDP and its real growth rate. If the measured inflation rate is low, the real GDP will be higher and vice versa, and along with that one also gets higher or lower numbers for productivity changes.

This statement is correct, but misses an important point. When applying a deflator, if improvements in quality are not adjusted in the deflator, they will not appear in real output measure. The best way to explain this is to consider a Ford factory that produced a million Model T Fords in 1920. The same factory is now producing a million Ford Mustangs. Say the price of Model T was $300 and the price of a Ford Mustang is now $30,000, the value of the output of the factory has increased from $300 million to $30 billion. However, the price index of these cars has risen one hundredfold.

If this price index is used as a deflator without any quality adjustment, the real value of the output of the factory will be.

30b/300m*300/30000 = 1

This result indicates that the output of the factory has not changed. If the number of people working at the factory was the same, no increase in productivity would be recorded. Most people would find these results hard to accept and claim that developing a Mustang took a lot of research and development and provides greater utility to the car owner. Although the factory is still producing a million cars, it is producing better quality cars.

The reason that output does not change is that all the quality improvements were captured in the price index. Although part of the increase in price from 300 to 30,000 is the result of an improvement in quality, no adjustment was made to the price index. Because all the quality improvement was captured in the price index, it is excluded from the resultant measure of real output.

The only way to feed to quality improvement into the real output measure is to quality adjust the price index. If it is assumed that a Ford Mustang is ten times better than a Tin Lizzie, the price index will show a only tenfold increase (rather than the hundredfold used above). The factory will now show a tenfold increase in real output. This is a more sensible result.

A good way to make this clear is to think about a Russian factory that was producing a million Ladas and a United States factory that was producing a million Ford Mustangs. Is their output equivalent? I suspect that most Americans would think that the American factory had greater output. The difference is a difference in quality.

So in general we expect improvements in the quality of products to be included in measures of real output and real GDP. But as already shown, this can only happen, if a quality-adjusted price deflator is used. It follows that if the quality adjustment in the price index is biased then the resultant measure of real GDP will be biased.

If the measured inflation rate is not adjusted for quality change, the real GDP will be too low, and along with that one also gets lower numbers for productivity changes.
Much of the drive for improving the methods of quality assessment used in price indexes has come from National Accountants who want better deflators for their estimates of GDP.

Price Indexes (10) Quality Adjustment

Some will say that the problem is with quality adjustment, full stop. They argue that the problem is not with the hedonic method, but with all quality adjustments, however they are made. To answer their concerns, I will explain why quality adjustment is necessary. The best way is to look at some examples. These will show that the adjustments made by statisticians actually reflect the way that consumers think when they are making purchases.

The most basic form of quality adjustment is an adjustment for a change in “quantity”. A good example is breakfast cereal. A common trick for cereal manufacturers is to keep both the size of the cereal carton and the price unchanged, but reduce the weight of cereal in the box. Many consumers will not notice, but the astute consumer will consider that the price of the cereal has increased. Some people take a calculator to the supermarket, so that they can get the best deal calculating the price per kilogram. The statistician makes a similar adjustment to the price to allow for the change in volume. If this were not done, the index would not record increases in cereal prices.

Now consider a more difficult example. Suppose a manufacturer of muesli or granola leaves the dimension of the package, the weight of cereal and the price unchanged, but changes the recipe by putting in less high quality grains and replacing them with low grade flour. Some consumers might not notice the difference, but those who do will choose a different product, because they think that the value for money has changed. The price of the granola is unchanged, but the consumer is getting a different product. In practice, these small changes might be impossible to measure, but the principle the statistician should make an adjustment to the price to reflect the change in quality.

These two examples show that the quality assessments made by price statisticians are similar to those make by consumers deciding which product to purchase. With other products the process may be more complicated, but the question is still the same: What value does the change have to consumers? Quality adjustment reflects the behaviour of consumers.

Price Indexes (9) Limited Use

In practice, the hedonic method is difficult to use, as statistically valid results are difficult to achieve. In general, the hedonic method has only been applied to cars, electronic good, and houses, because the different features are relative standard and a large sample of models are available in the market. Four important points should be noted.

1. A quality adjustment is only done when one product in the matched sample has to be changed. This will only be a small percentage of the total sample. Most products have remained unchanged for many years. For example, electricity, meat, milk, toilet soap, haircuts, bus travel have not changed much from when my grandfather purchased them.

2. Overlap Pricing is used in most situations where substitution is necessary. The only subjectivity is in deciding where Overlap Pricing is not possible, because both the old and new products are being sold in significant numbers.

3. The Hedonic Method is only used for products that need direct quality adjustment, so only a very small percentage of prices are adjusted this way. Some critics state that an hedonic adjustment is made to every price collected. This is a great exaggeration.

4. Hedonic adjustment may result in a smaller or larger adjustment than the traditional method. This means that the common complaint that hedonic adjustment method will reduce the increases in a price index is unfounded. The introduction of the hedonic method may actually increase the price index.

Given these four points it is hard to see what all the fuss is about.

Price Indexes (8) Hedonic Methods

Direct Adjustments for quality change are difficult to make without introducing subjectivity or bias. Consider an example. If the only difference between the old and the new car is a catalytic converter, a direct assessment of its value to consumers must be made.

Most information about the cost and perceived value of the catalytic converter will come from the manufacturer, who is likely to have a biased view. This is why statisticians prefer not to make direct adjustments. Contrary to popular opinion, hedonic adjustment has been introduced to make direct quality assessments more objective.

To apply the hedonic method, index statisticians collect the prices of as many cars as possible that are available with and without catalytic converters. A regression is then used to calculate how much difference the addition of a catalytic converter makes to a car.

In principle, the hedonic method is more objective than direct adjustment, because information from the market place is used to estimate the value of a so-called quality improvement. Using information from the market will generally be better than depending on the judgments of statisticians and information from suppliers. For example, critics often argue that statisticians place too higher value on things like extra memory on a computer.

The hedonic method deals with this issue by attempting to use market prices to assess how much consumers are willing to pay for extra memory. If extra memory is of no value to consumers, this should be reflected in the hedonic measure. This should be better than a subjective “direct assessment” by a statistician.

Price Indexes (7) Overlap Pricing

The most common solution to the problem described in the previous post is to make the change before the old product disappears. Then the old product and new products can be surveyed in a cross-over period. A price relative for the old product is used to calculate the price movement up to the crossover period. A price relative for the new product is used to measure the price movement going on from the crossover period. This ensures that the matched sample used to calculate the price change between any two periods actually matches. This method is called Overlap Pricing.

This is where quality adjustment comes. A noted, the old and new products will quite likely be of different quality. The Overlap Pricing method assumes that because the two products are selling in the same market at the same time, the difference in price between the two products reflects the difference in value to consumers between the two products. If this were not true one, one of the products would stop being sold.

The Overlap Pricing method is the preferred method where the sample of prices has to be changed because the market decides the value of the difference between the old and new item.

There are some situations where the Overlap Pricing method is impractical. Sometimes when a new model is introduced to the market the old model is completely sold out before the new one is introduced. Or if the old one is still available, it might be so unpopular that it has to be massively discounted to clear the old stock. This is generally the situation with cars, stereos televisions and computers.

Statisticians cannot assume that the difference between the two products is reflected in their price difference, so they have no choice but to make a judgment about how much of the difference in price is the result of differences in quality and how much is genuine price change. This method is called Direct Adjustment.

Price Indexes (6) Changing World

The problem with the matched sample is that the world is not static. The range of goods and services available is constantly changing, and people are constantly changing what they buy. The best solution to this problem is to update the basket as frequently as possible.

Households are constantly searching out the cheaper outlets for the goods and services they by. Since this shift to cheaper outlets and brand is not captured by the price index, most fixed basket indexes have an upwards bias. In other words, they overstate the level of price change.

Some economists get agitated about chain-linking of price indexes, but chain-linking is just a practice of updating the sample basket and weights more frequently. This partly removes the upward bias that comes from leaving the basket unchanged.

The ongoing challenge faced by price statisticians is that some of the goods and services in their matched samples go out of production or become redundant. When this happens the redundant product must be substituted with a different product. In some situations the substitute might be quite different, so a price relative with the price for a new product in the numerator and an old product in the denominator would distort the price index.

Price Indexes (5) Choosing a Basket

The choice of the basket is really important, so the selection process is usually based on a family or household expenditure survey. This ensures that, as far as possible, the basket is representative of the goods and services that households actually buy. This expenditure information is also used to ensure that each good and service is assigned a weight that reflects its importance in household budgets.

Choosing the basket of goods and services and list of outlets to be included in price surveys is the most difficult part of designing a price index. Any bias that is introduced will reduce the accuracy of the index. If price statisticians really wanted to fiddle the index, this is where they would do it. Selecting samples gives far greater opportunity for mischief than the much maligned hedonics.

The BLS attempts to reduce bias by using random samples of goods and services in all price surveys. Most other countries cannot afford this expense and use purposive sampling, which may introduce bias if care is not taken. However, the issues around designing robust random and purposive samples are well understood.

Price Indexes (4) Scope of Measurement

Most price indexes measure the change in the price for a fixed basket of goods and services, because that is all that can be measured. Because the world is not static, this means that the price index will not a perfect reflection of Statisticians are generally clear about this, and they focus their energies on measuring what the index purports to measure accurately, rather than trying to measure something else. This is why the matched sample is important. Price statisticians put a lot of effort into ensuring that the basket of goods and services is the same in each period.

If the quality of the goods or services being surveyed is allowed to change from period to period, the index will no longer be measuring a fixed basket and no one will no what it is measuring.

For example, a CPI measures the change in price of the goods and services that households buy. It does not purport reflect the experience of any household, because everyone is different. It cannot measure the true cost of living, whatever that is. All it is designed to do is measure the change in prices of the goods and services that households buy. People do not need to use this measure if they do not like what it measures, but it should not berated because it does not measure something that cannot be measured. I do not take my new car to the dump, because it cannot fry eggs.

Price Indexes (3) Level or Change

Economists are interested in measuring the overall price level. Unfortunately, measuring the price level in an economy is impossible. This is an important point that underlies the design of all price indexes. The prices of a pint of milk and a Ford V8 cannot be averaged because the units are different. However, we can measure the change in the price level, by converting the prices to price relatives, that all have same units. The assumption behind this practice is that variability in price change will be less than the variability in absolute prices. Lower variability reduces the sampling error.

The basic method for calculating a price index is to choose a representative basket of goods and services. The prices of all the goods and services in this basket are measured in the current period and a previous period. This is referred to as a “matched sample”. The change in prices recorded for this matched sample is used to calculate the price index.

With a matched sample there is a standard unit. The current price for each good or service is divided by the previous price. This ratio is called a price relative. If there is no price change, the price relative equals unity. So there is a common measurement rod, as all changes are measured relative to unity. The price index shows price change relative to unity (or a base of 100 or 1000 to show more significant figures).

Price Indexes (2) Estimates and Approximations

The difficulties of price index measurement have been well understood for almost a century. Statisticians have always understood that price indexes, like all statistics are estimates.

Statistics are different from accounting. Unlike accountants, who add up every transaction to produce detailed accurate accounts, statisticians make estimates based on partial information. There is nothing wrong with making decisions based partial information; we all have to do that all the time. Statistics is just a way of systematising partial information to clarify what it means.

All statistics are estimates or approximations. The hard part is determining if these approximations produce something useful. Statisticians put a lot of effort into measuring the accuracy of the statistics they produce. Users of statistics and economic commentators can then decide if the approximations are good enough for their purposes. Serious problems arise when they treat statistics as if they were exact measures.

This issue becomes clear with respect to price indexes, when we remember that in any economy, billions of transactions take place every day. Millions of different goods and services are sold in different quantities at different prices. Recording and measuring all these transactions is impossible. Calculating an average price of all the transactions that occur in the economy in one day just does not make sense. The only way to measure prices is to do what is done with most statistics and that is to take a sample.

This is not an unreasonable course of action. Supermarkets generally charge all customer the same price for a size and brand of baked beans, so it is not necessary to observe every single transaction to understand what is happening to the price of baked beans. However, sampling does introduce sampling error so a price index can never be an exact measure.

Price Indexes (1) Hedonic Histrionics

From time to time I come across articles about the use of hedonic methods in price indexes. The topic is popular among conspiracy theorists and the Consumers Price Index (CPI) produced by the US Bureau of Labour Statistics (BLS) seems to draw the most heat. Changes in the methods used in the CPI are often portrayed as part of a government cover-up.

Economists get quite stirred about this issue too and often perpetuate confusing ideas about something they do not fully understand.

The PPI has clearly been insufficiently adjusted with hedonics, chain-weighting and rental equivalence (Stefan Karlsson).

Then, when one adds in hedonics, which strips out many price increases by assuming they are quality improvements, and when one factors in the substitution allowances in the data, it is clear that the CPI is not going to flash any sort of alarm bells (Bill Fleckenstein).

One problem that makes the discussion confusing is failure to distinguish between two terms: “quality adjustment” and “hedonic adjustment”. Quality adjustment is a practice used in most price indexes. Hedonic adjustment is just one among a variety of methods used for quality adjustment.

The BLS did not introduce quality adjustment when it started using hedonic methods in the 1990s. It has used quality adjustment as long as it has produced price indexes (I will explain why in a later post). The change made in the 1990s was to introduce hedonic methods to quality adjust a few commodities, where the BLS was unhappy with other methods of “quality adjustment” (Brent Moulton).

More on this in the next few posts.