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Do UK price indexes overstate inflation?

Official price indexes may overstate (or understate) inflation for a number of reasons. These include substitution bias, outlet bias, failure to allow properly for quality change, and failure to allow for new goods. This note finds that substitution and outlet bias are probably not significant sources of error in the UK. The other two sources most probably do lead to significant overstatement, but the size of the upward bias cannot at the moment be quantified.

'Since, with technological advance, the quality of products tends to improve, the estimates of consumers' expenditure tend to understate the true growth in standards of consumption'. (CSO 1985, p. 72).

'The Producer Price Indices ... make some allowance for changes in models and specifications when these can be identified in terms of changes of cost or in technical performance. ... [Allowances for quality change] are necessarily somewhat rough and seldom fully satisfactory'. (CSO 1985, p. 40, emphasis added).

1. Introduction(1)

The issues

It is widely believed that official price indexes overstate inflation, primarily because of unmeasured quality change. This view has some official support as can be seen from the two quotations above from the CSO's Sources and Methods volume. There are various estimates for other countries of this overstatement, ranging from less than 0.5 per cent to 2 per cent per annum.(2) If inflation is overestimated, it follows that real growth is underestimated. One of the purposes of this note is to see whether there is in fact any hard evidence for an over-statement of inflation as large as 2 per cent.

There are three principle issues. First, do existing indexes allow adequately for changing (most people think, rising) quality levels? Second, how should new goods be incorporated into a price index? Third, do existing indexes give adequate coverage of the economy?

Most but not all of recent research on price indexes has been devoted to the first issue and much progress has been made. The second issue however is the more difficult and the one on which very little progress has been made. The third issue, coverage, is more mundane and for that reason has attracted less interest, but may be just as important in practice.

The importance of accurate estimation of prices can hardly be overstated, because of the numerous uses to which price indexes are put. First, price indexes are basic to all forms of economic analysis of the economy whether done within government, or outside by academics, by analysts or journalists. Most economic relationships are specified as being between quantities, not values, since economic behaviour is believed to depend on relative not absolute prices. Hence knowledge of quantities, which may be best obtained by deflating values by the appropriate price indexes, is essential to economic analysis. Second, policy and public opinion is greatly concerned with the rate of inflation, so here price indexes have a direct and obvious interest. The government's macroeconomic policy is now focused around its target band for inflation, which is defined specifically as maintaining the Retail Prices Index (excluding mortgage interest payments) in the range 1-4 per cent per annum and eventually reducing it to the lower half of this range. Third, official price indexes have a statutory role. The RPI is used to uprate social security and National Insurance benefits and also the interest and capital value of index linked gilt edge stocks. Fourth, the RPI and the Producer Price Indexes (PPIs) are widely used by the private sector in wage and contract negotiations.

Concepts of price indexes: what are we trying to measure?

Three different concepts of price index have been discussed in the literature: the axiomatic, the statistical, and the economic. The axiomatic approach was pioneered by Fisher (1927). An index number is a sort of average and should be chosen so that it satisfies a number of tests (Diewert (1987) suggests ten), for example, it should be invariant to changes in the monetary and quantity units. Unfortunately, it has been shown that no index number formula satisfies all the suggested tests. If one or more test is dropped, then more than one formula can satisfy the remainder.

According to the statistical approach, traces of which can also be found in Fisher (1927), a price index number should be regarded as the central tendency of the sample of price changes which we observe. This approach has recently been revived in the study of measures of inflation (Bryan and Cecchetti 1993). Unfortunately, this approach also suffers from non-uniqueness (Selvanathan and Prasada Rao 1994).

According to the economic theory of index numbers, an index like the RPI should aim to measure the cost of living. Modern theory regards the cost of living (COL) index as the ratio of two expenditures, the numerator being the minimum expenditure at the new set of prices which would put the consumer on the original level of utility, and the denominator being the chosen expenditure at the original set of prices. More precisely, the increase in the cost of living between any two periods is the extra cost of achieving a reference level of utility (a particular indifference curve).(3)

Official price indexes do not necessarily conform to the economic concept of index numbers, even in intention. The RPI Advisory Committee (1986, para 6) nailed their colours to the mast: 'We wish to reaffirm the view taken by our predecessors that the RPI is an index of price changes and not a 'cost of living' index.' [Italics in the original]. The UK is not alone in defining its CPI as a price change index - for example France, Australia and Japan follow the same approach. By contrast, the US CPI is defined as a COL (Fixler 1993; US Department of Labor 1992, p. 177). It would of course be possible to regard the RPI just like the US CPI as an approximation to a true cost-of-living index, while recognising that practical considerations, such as the need for timeliness and the undesirability of revisions, as well as theoretical difficulties, limit the closeness of the approximation. In fact, somewhat paradoxically, the RPI may be in practice a closer approximation to a true COL index than is the US CPI, because of the much more frequent changes in the weights in the former (see below).

Statements like 'The RPI is biased upwards' or 'Inflation is overstated' imply a comparison with a true index. Unless the notion of a true index is to be purely subjective, existing indexes must be assessed in the light of the only existing objective standard, which is provided by the economic theory of index numbers. In the case of the RPI, the comparison must be with a COL index.

Examples of alleged bias include (a) substitution bias - failure to allow for consumer substitution away from more expensive goods; (b) outlet bias - failure to allow for consumers shifting to less expensive types of retail outlet; (c) failure to allow for quality change; and (d) failure to allow for new goods.

Plan of the note

Before going on to discuss the issues outlined above, I first describe briefly the price collection process in the UK. Section 3 then looks at substitution bias. Sections 4 and 5 are devoted to quality change. In section 4, I consider the various methods employed in the UK and the US for capturing quality change, including the hedonic method which is employed officially in the US but not as yet here. How well these methods have worked in practice is the theme of section 5, where will be found an evaluation of the important work of Gordon which is highly critical of the results of official US efforts. The extent to which Gordon's criticisms are valid for the UK is considered.

Section 6 looks at the issue of how, if at all, price indexes should allow for new goods and increased variety. The theory is outlined, and the question of whether it is practical to implement is discussed. Section 7 looks at outlet bias, which can be thought of as a quality problem, and also as a new good problem.

A price index may be excellently administered but will nevertheless be of limited interest if it only covers an unrepresentative part of the economy. Section 8 therefore analyses the coverage of the economy by price indexes, both on the output and the expenditure side.

2. The Price Collection Process In The UK

The RPI(4)

Prices for the RPI are collected for around 600 'items'. The list of items to include is reviewed every year, and about 50 changes are typically made. Some 150,000 price quotations are obtained each month. The basic starting point in the construction of the RPI is the set of elementary or micro-indexes. The indexes are constructed from price data at item level by area and shop type, without using any explicit weights. Item indexes are weighted together to produce indexes successively at section, group and supergroup level. There are 84 sections, 14 groups and 5 supergroups. National item prices are calculated using regional weights from the Family Expenditure Survey [FES] and (national) shop type weights, the latter from the Retailing Enquiry. National item prices are weighted together to form section indexes using weights from a variety of sources (for example, the FES, and the National Food Survey). To obtain group indexes, weights are obtained from the FES. The reference month is January. However section weights relate to the FES results for the 12 months up till the preceding June, uprated by the change in the appropriate indexes over this period.

Until recently, the price collection process was carried out in Great Britain by 175 Unemployment Benefit Offices (UBOs); Northern Ireland was covered by an additional 5 areas. Since the beginning of this year, price collection is done by a private company, Research International, in 178 locations and by the CSO itself in two locations. These 180 areas were selected in the 1940s as representative of the country and cover what are now the 12 Standard Regions. Two types of shop are distinguished, 'multiples' and 'independents'. In addition, the prices of some 100 items are collected centrally. These include gas, water, newspapers, council rents and rail fares, also prices from multiple stores with a national pricing policy.

In some cases an item is the name of a specific brand, for example, a particular manufacturer's chocolate bar. But in most cases an item is a brief description ('washing machine'). It is up to the price collector to decide whether a particular product on sale in a particular shop corresponds to an item on the list. However, once a particular product has been selected as fitting the description, the same product must be priced in every successive month in the same shop, at least until the process starts again the following January. If this cannot be done for some reason, for example, the shop has closed or the product in question is not stocked any more, the fact is notified and one of several procedures come into play. If a replacement item is available, this can be substituted.

When a substitution occurs, three possible courses of action are available. (1) The collector can attempt to estimate the quality difference between the original and the replacement item. This alternative is rarely followed in practice (RPIAC 1986, p. 58). (2) A January price is imputed for the substitute on the basis of movements in the price of similar items. This means that any difference in price between the original and the substitute product is attributed to quality change. (3) The substitute and the original product are judged to be comparable for practical purposes, so any difference in price between them is judged to be a price rise. Currently, I am informed, there are some 2,300 cases per month where the second alternative is adopted and 1,900 where the third is adopted (out of roughly 150,000 prices quotations per month).

Following the discovery of a computer programing error which led to a miscalculation of the RPI (at that time administered by the Department of Employment), the National Audit Office [NAO] investigated the administration of the RPI. Their report revealed a number of rather worrying deficiencies in the management of the data collection process, for example failure to carry out adequate checks on the accuracy of the price quotations (National Audit Office 1990).

Since the NAO scrutiny and the transfer of responsibility for the RPI to the CSO, the latter has instituted a review and tightened up the monitoring of the price collection process quite considerably. The CSO has put in place a network of regional coordinators who backcheck prices. Local office managers also check batches and the CSO makes its own checks centrally. These improvements of course only affect prices collected since the new procedures were put in place.

Some of the NAO findings are relevant to two important issues, outlet bias and the speed of introduction of new goods onto the index.

Outlet bias. There are two main sources of possible bias in the shop types chosen (at that time) by UBOs. First, the geographical pattern of the chosen UBOs, determined in the 1940s, may no longer be representative of the country. As part of the programme of improvements currently introduced by the CSO following the market test of the local price collection, a new probability sample of locations and outlets will be phased in over the next three years. Second, the retailing inquiry yields information only on a national, not a regional, basis. However, the FES now collects information on the shop where each purchase is made, which should reveal any regional variation.

New goods. As stated above, the 600 or so items are reviewed annually, but nothing has been published about the frequency with which new products are added. The NAO did note however that microwave ovens were added to the list in 1988 (para 2.7), which in this instance would suggest a fairly speedy response to the arrival of a new product.(5)

The PPI(6)

Currently, some 11,000 price quotations from 3,000 manufacturers are collected per month. Prices are collected by means of 'shuttle cards' sent to participants which they fill in and return. It is made clear that actual (transaction), not list prices, are required, but there still seems to be some doubt as to whether firms always report the former (CSO 1993a, p. 20). Prices are meant to be for 'home sales', not exports. Whether firms always distinguish between domestic and foreign sales (indeed whether they always know which are which) is again unclear. The participating firm picks the item on which it will report. There is a space on the shuttle card to indicate any change in the specification.

Over time the number of items for which price quotations were sought has varied. This variation has however had nothing to do with the number and variety of goods on offer from UK manufacturers, but has instead mainly reflected the resources devoted to the PPI.

Up till 1991, firms participating in the PPI did so voluntarily. Since then, participation has been compulsory. The CSO does not attempt to sample firms randomly but deliberately picks larger firms on efficiency grounds, since larger firms by definition have a larger market share. Participating firms currently account for about 40 per cent of manufacturing sales, though the products on which they report necessarily account for a much smaller proportion.

Despite the fact that the PPI is now statutory, there is still a considerable voluntary element since it is up to the firms to notify changes in specification or model changes. Normally, the CSO does not make visits to firms, so it is reliant on firms accurately reporting any significant changes. However, the pattern of price changes is monitored so large changes in price will trigger an enquiry as to whether the item reported is genuinely unchanged.(7)

Once a firm had picked an item, it was until recently under no pressure to change it, even though its importance or representativeness may have changed. The PPI Review concluded: '... more effort needs to be spent to ensure that items of declining importance are replaced' (CSO 1993a, p. 19). Following the Review, the CSO has decided to become more proactive in ensuring items are up-to-date. A letter was sent to all contributors in 1993 emphasising the point. This produced a large number of changes to items, and it is expected that this exercise will be repeated regularly. In particular the point will be highlighted in the PPI shuttle card (soon to be replaced by a form).

Quality change is dealt with in a number of ways. In 1992, 1,460 changes in specification were reported amongst the 11,000 items whose prices were reported. Of these 1,460:

In 722 cases, any changes in price were determined to be due to quality change.

In 236 cases, there was adjudged to be no change in quality.

502 cases were adjudged to fall into an intermediate category.

However, the CSO has found that car manufacturers at least tend not to report small quality changes (CSO 1993a, p. 16).

In evaluating the CSO's efforts to account for quality change, one should always bear in mind that the resources available are quite small. The annual central government cost of the PPI is about [pounds]1.4m. This is quite a trivial sum in comparison with the cost of other data-gathering projects, for example the UK's contribution to CERN.

3. Substitution Bias

Substitution bias is the difference between a consumer price index and a COL index. It arises with base-weighted indexes since they measure the cost of buying a given basket of goods in the base year, not the base year level of utility.

Some terminology is helpful: a Laspeyres price index is an example of a fixed weight index. It may be either fixed base or chained.

The Laspeyres price index is:

[L.sub.tb] = [p.sub.t][x.sub.b]/[p.sub.b][x.sub.b]

where p is the vector of prices, x a vector of quantities and subscripts indicate time: t is the current period and b is the base period. The Laspeyres price index measures the increase in the cost at time t of buying the base period basket of goods and services. The Laspeyres is fixed weight in the sense that in calculating the index for time t, only base period quantities are used in weighting, not those of t or any other period. It is fixed base if the base period is the same whatever the current year. It is chained if the base year b equals t - 1, that is, if the base shifts up as t rises.

The UK RPI is a chained Laspeyres index since it uses January weights to calculate the monthly index for each subsequent month in the current year. The weights are revised in line with the results of the Family Expenditure Survey each year.(8) The monthly figures for each year are linked on to the index for the preceding year using January as the link month. The UK PPI is also a sort of chain index, since the weights are changed every 5 years (though the possibility of moving to an annual chain index in the near future is currently under study (CSO 1993a, pp.3 and 21))). The index values using the new weights are linked on to the index values using the earlier weights. On the other hand the US CPI is fixed base Laspeyres. The weights are updated very infrequently and when this is done the whole series is recalculated using the new weights; the old weights no longer affect any of the index values. US national income and product accounts in constant prices also employ the weights of a single year, which is periodically changed, and thus differ conceptually from the corresponding UK accounts.

The Laspeyres price index is often thought of as a pessimistic measure of inflation. It overstates the rise in the cost of living (COL) since it does not allow for the possibility of substitution away from goods whose relative price has risen.(9) This of course assumes that we know what the 'true' measure must be. Economic theory suggests that the correct criterion is the cost of purchasing the base year level of utility rather than the cost of purchasing the base year basket of goods. The divergence between an empirical price index and this theoretical concept of the COL is known as the substitution bias of the index.

The best known study of substitution bias is Manser and McDonald (1988). Their basic data consisted of annual prices and quantities of 101 commodities making up the bulk of US personal consumer expenditure over the period 1959-85. They compared the performance of the Laspeyres index, both fixed weight and chained, against theoretical measures of the true COL and found that the bias was small. The fixed base Laspeyres exceeded the 'true' measure by between 0.14 per cent per annum and 0.22 per cent per annum during a period in which the index rose at 2.50 per cent per annum. The bias in the chained Laspeyres was negligible, no more than 0.01 per cent per annum (see their Table I).

It would seem worthwhile to repeat their study on UK data using first a similar level of aggregation and then going to a more detailed level. However, it seems quite likely that the bias will be revealed to be small, at least for the RPI, simply because the UK weights are changed every year. One would however expect a larger bias for the PPI in its current form, since the weights are changed less frequently (at the moment every five years, though it is planned to move to annual changes in the near future).

4. The Treatment Of Quality Change: Alternative Methods

The importance of quality change

Quality can go up or down, but there are good reasons for thinking that in a market economy the trend is generally upwards. The reason is that product improvement is a basic competitive strategy. A producer who can improve his product will outsell rivals. Under competition, the pressure for improvement is always present, creating a presumption that quality will rise over time. It is true that the process of economic growth also frequently involves the introduction of cheaper, lower quality, substitutes for established products. An example would be paper tissues competing with linen handkerchiefs. But in this case the higher quality product generally survives, so here we have an example not of falling quality but increasing variety (see below).

There are however occasions when quality will fall, even under competition. If the price of an input rises, then producers will increase the use of cheaper substitutes, and this may entail a loss of quality. Consumers may prefer to accept a lower quality product rather than pay a higher price for the product under its original specification. For example, if the price of plastic rises then car manufacturers may employ more steel even though this results in a heavier and more rust-prone vehicle.

However, the only input whose price consistently rises over time is labour. So it is the quality of labour intensive services, whether sold on their own or bundled together with some other product, which we may expect to see shrinking. The best example is probably retailing where, as has often been pointed out, the measured rise in productivity is partly due to getting the consumer to do more of the work: the consumer drives to the store, instead of the goods being moved to within walking distance, and information about the products is obtained by reading the labels rather than asking the shop assistant. Some public services suffer from the same disadvantage, as well as not being under the same market pressure for improvement.

The other important exception to the trend towards quality improvement is when a major change in technology occurs, such as the introduction of mass production into what was previously a craft process. The early model T Ford was, notoriously, only available in black. The post second world war shift from small bakeries to mass production led to tasteless bread. Early computerised typesetting was crude and ugly by comparison with the best of hand typesetting. In all these cases, the new technology was not able to rival the old in all respects but had an overwhelming advantage in cost. But in each of these cases we can now see that the loss of quality was temporary.

It is often thought that quality change is particularly important for durable goods, particular those where technical progress is rapid such as computers. But there is plenty of evidence for quality change in durables of mature technology. Gordon (1990) gives many examples of quality improvements in refrigerators and in cars we observe a 'trickle down' effect under which features previously available only on luxury models start to appear on mid-range and even bottom-of-the-range models. A characteristic feature of durables is that new features are constantly being added. Over time, reliability and running costs typically fall. General usability may rise too as for example weight is reduced. But the fact that quality change is clear and ever-present in durables should not lead us to ignore its existence for non-durables.(10)

Whether the view that quality is generally rising is accepted or not, quality change clearly raises important issues for price measurement and it is to these that we now turn.

The matched models method

The method of quality adjustment almost invariably used in practice by statistical agencies is the matched models, or matched brands, method. The aim is to select a representative model or brand and track its price over time. Provided that the brand or model remains physically identical, the quality problem is solved since an item of constant quality is being priced.

Agencies differ however in the method of selecting models or brands. In the US, specification pricing is the rule: a detailed physical specification is drawn up for every item. It is the job of those collecting consumer prices or firms supplying producer prices to find products which fit the specification. In the UK by contrast more discretion is allowed to price collectors and suppliers. As we have seen, for the RPI the items are names (either generic or occasionally brand names); for the PPI inquiry (which is now statutory), there is no list but firms are left to volunteer products for inclusion in the index.

When the specification changes or a model or brand is discontinued, there a number of possible ways to proceed:

(1) Ignore the change in quality if it is judged to be small.

(2) Assume that the substitute product has risen in price at the same rate as comparable products. This amounts to ignoring this product when calculating the current value of the index (This method is called rather confusingly 'deletion' in the US literature).

(3) In the case where the old and new model are sold simultaneously, the new model can be linked to the old one. The difference in prices at the given date is the measure of quality change.

(4) Include the new product, but with a quality adjustment. The latter could be based on (a) judgement or (b) information from producers on the cost of the quality change. This last method has been applied particularly to cars, where prices of optional extras are frequently quoted.

Each of these methods may give rise to biases and the direction of bias is not always clear a priori. In the case of (1), ignoring a whole series of small changes may eventually lead to a large over-estimate of prices. However, a negative bias is also conceivable.

Use of (2) implies the assumption that the change in price of products of constant quality is the same as that of products of changing quality. Again, the direction of bias, if any, is unclear.

(3) seems the most satisfactory in principle but suffers from the practical difficulty that the old model may be withdrawn at the moment that the new one is introduced and hence the method cannot be applied. This is likely to be a particular problem in technically fast-moving areas like computers and consumer electronics.

(4) obviously depends for its success on the degree of co-operation which can be secured from manufacturers.

The hedonic method

The hedonic approach assumes that goods are valued by consumers for their underlying characteristics (Rosen 1974; Griliches 1990; Triplett 1990). A good's price depends on the quantity of each characteristic which it embodies. In a typical application of the hedonic method, data on the characteristics believed important in a particular good would be gathered and the data pooled for two consecutive time periods. The following regression would be run:

log [p.sub.it] = [Alpha] + [C[prime].sub.it][[Alpha].sub.c] + [[Alpha].sub.d][D.sub.2] + [u.sub.it], t = 1,2; i = 1,...,N

where [p.sub.it] is the price of the ith product, [C.sub.it], is a vector of quantities of characteristics embodied in the ith good, [u.sub.it] is an error term, and [D.sub.2] is a dummy variable for the second time period. The estimated rate of inflation for this sort of product, after allowing for quality change, could then be read off from the coefficient on the dummy variable, [[Alpha].sub.d]. The same regression could be run on a rolling basis, to estimate inflation in consecutive years.

Most hedonic studies have been done on durable goods and have used only the prices of new models. Hall (1971) suggested extending the technique to include current, second hand prices of older models as well. The age of a model will now be an additional right hand side variable (to allow for declining physical efficiency with age). This extension of the technique seems clearly useful in principle, since it allows more data to be brought to bear. A simple version of his idea is:

log [p.sub.its] = [Alpha] + [C[prime].sub.it][[Alpha].sub.c] + A[prime][[Alpha].sub.s] + [[Alpha].sub.d][D.sub.2] + [u.sub.its], t = 1,2; i = 1,...,N

where [p.sub.its] is the price at time t of model i of age s and A is a vector of model ages.(11)

Despite the theoretical attractions of the hedonic method, there are some inherent limitations. It is never possible to be sure that all relevant characteristics have been included. Suppose a relevant, desirable characteristic has been omitted and this characteristic is uncorrelated with the included ones. Suppose too that it rises in the second period. Then the estimate of [[Alpha].sub.2] will be biased upwards (Gordon 1990, p. 93).

The hedonic method has been employed officially in the US for many years to estimate a price index for housing costs and more recently to estimate one for mainframe computers. Experiments are under way to do the same for microcomputers (Berndt and Griliches 1993; Berndt et al. 1993) and use of the method is likely to spread. Compared with the methods which preceded them, the effect of adopting the hedonic method has been dramatic. Mainframe computer prices are now shown as declining by around 20 per cent per year, where the previous rate had been assumed to be zero, and this produces large effects on estimates of the capital stock and of the growth of GDP. Prices of microcomputers show comparable or even higher falls.

Hedonic methods have yet to be adopted officially in the UK though studies of computer and car prices have been commissioned by the CSO.

The great strength of the hedonic method is that it can make efficient use of the data. With the matched models method, if a model is discontinued, the previous prices of this model become irrelevant to the future index. The limiting case is where every model changes every year, in which case the matched model method breaks down completely (unless manufacturers can supply evidence of the cost of specification changes). But the hedonic method could still work provided there is sufficient cross-sectional variation in characteristics.

The reason why hedonic methods seem irresistible in fast-moving areas like computers can be illustrated by some figures given by Berndt et al. (1993, Table 2). They measured the characteristics of 630 models of PC in 1992 and 453 in 1991, but only 14 of the 1992 models could be matched with 1991 models. A matched model approach obviously risks measuring price changes in models which only account for a very small part of total expenditure and which may be very unrepresentative of current consumer tastes.

Nevertheless, it cannot be concluded that hedonic methods are invariably superior to the matched models method. Hedonic methods have been criticised for producing results which are implausible and not robust. Once again, everything depends on the way that the method is implemented. A difficulty with some hedonic studies is that it is far from clear that the characteristics which consumers truly value have actually been identified. For reasons of data availability, proxies often have to be employed. For example, early hedonic studies of cars used weight as a proxy for quality. However, there is a danger that the hedonic method may be criticised unfairly simply because its workings are more open to outside scrutiny, far more so than the matched models method (Triplett 1990).(12)

5. The Treatment Of Quality Change: Practice

Gordon's critique of official US durable goods prices

The whole subject of the accuracy of official price indexes has recently been opened up by the massive work of Gordon (1990). It is important to note that, though Gordon did use some innovative methods for some of his results (for example, the hedonic technique for computers and cars or unit value indexes for diesel engines), the bulk of his findings results from applying methods which are very similar conceptually to the official ones.(13) In other words, he employed 'specification pricing' or the 'matched models' method but using publicly available data such as the Sears mail order catalogue or the information in Consumer Reports (the US Which?). His book contains also case studies of commercial aircraft, electric utility generating equipment, computer processors and peripherals, electrical appliances, and new and used automobiles.

His main findings for the period 1947-83 were as follows: (1) the official deflator for producers' durable equipment (that is, plant and machinery) overstates the growth of prices by nearly 3 per cent per annum (his Table 12.2). (2) the official deflator for consumers' durable expenditure overstates the growth of prices by about 1.5 per cent per annum (his Table 12.10). The difference between his estimate of the biases in the two indexes may reflect the fact that Gordon's coverage of producers' durable equipment was quite comprehensive, while he was only able to cover categories of consumer durables accounting for about half of all such expenditure. The figure of 1.5 per cent for the consumer durable bias assumes that the official indexes for the uncovered half are correct.

The effect on the national income accounts of his revisions is quite dramatic. He finds that using his new indexes consumer durable expenditure grew at 6.01 per cent per annum over 1947-83, not 4.48 per cent per annum as the official figure would have it (his Table 12.11). Expenditure by producers on durable equipment over the same period grew at 6.15 per cent per annum, in contrast to the official figure of 3.19 per cent per annum (his Table 12.4).

Gordon's study was entirely devoted to durable goods. Even here he does not claim to have quantified all the quality improvements which he believes occurred. The effect of applying his methods to non-durable goods prices must remain a matter of speculation. But accepting the official price indexes for non-durables as correct his new indexes for durables produce equally dramatic effects on some familiar ratios. For example, instead of remaining roughly constant, the ratio of investment in producers' durable equipment to GNP roughly triples over this period and the ratio of the stock of producers' durable equipment to GNP rises by 406 per cent, instead of by only 75 per cent (his Tables 12.5 and 12.6).

On the other hand, because the two categories of expenditure he considered, consumer durables and producers' durable equipment, constitute only about 15 per cent of GDP, the effect on the overall GDP deflator of his revisions, on the same assumption that other non-durables price indexes are correct, can be calculated to be fairly small: his new estimates would reduce its growth over 1947-83 by about 0.33 per cent per annum. Since the proportion of durables spending is similar in the UK, if his results were replicated here they would result in a comparable effect on the UK GDP deflator.

How are we to judge who is right, Gordon or the official agencies he criticises? Though no doubt Gordon's work can be criticised in detail, the overall conclusion that official US agencies have seriously underestimated quality change is hard to resist, for several reasons. Gordon presents evidence from a great variety of sources both statistical and anecdotal, all tending to the same conclusion. His evidence is from data sources which are in the public domain and which he describes very fully. His calculations are in principle replicable by others. By contrast, though we know something of the official methodology, the data on which official indexes are based is largely confidential. For these reasons, Gordon's main findings seem to have won general acceptance, even from those who would be well-placed to refute them if they contained any obvious flaw (see for example, the review by Triplett (1993)).

To reiterate, Gordon's conclusions were mainly reached by applying the same basic methods as the BLS (matched models and specification pricing) and did not rest to any great extent on the use of hedonic or other 'high tech' methods. His investigation in fact amounts to a large scale replication of the BLS's work. Accepting then the main thrust of his conclusions, how did the BLS come to make such a poor job of applying its own methodology? This is a question which cannot be answered with any degree of certainty, not even by the BLS, since for confidentiality reasons the Bureau's own past price quotations are apparently not available to its own current staff. But we may speculate that it was through some combination of failure to ensure that specifications are kept up to date so that obsolete products are not given undue importance and failure to check that cooperating firms notify changes in specification or the introduction of new models. Gordon points out that one of the weaknesses of the BLS method is that, though firms are required to notify changes in the model whose price they are reporting, they are not required to notify the BLS when they introduce a new model. Hence the firm may from inertia continue to report the price of an unrepresentative product after it has in effect been replaced by a newer model. By contrast, mail order catalogues, on which Gordon relies, speedily drop models which cease to sell in large numbers. Though there was a considerable reorganisation of the BLS price gathering process in the 1980s, for the same reasons we cannot be sure that the same errors are not continuing to be made.

The UK treatment of quality change: an assessment

Short of actually carrying out an exercise like Gordon's for the UK, there is no way of knowing whether or to what extent quality change is underestimated in UK official price indexes. But the US example certainly makes it seem likely that some significant underestimation occurs.

The UK and US methods of treating quality change are similar as we have seen, though implementation differs in detail. In principle, there is no reason to expect these methods, usually the matched models method, to lead to biased estimation of quality change. Nevertheless Gordon's results show that the BLS (at least in the past) has systematically underestimated quality change in durable goods. This does not prove that UK indexes suffer from similar biases, since everything depends on how the methods are implemented in practice.

As far as the PPI is concerned, UK methods seem to suffer from the same potential practical weaknesses as Gordon suggests afflicts US ones. In addition, the UK is in a less favourable position for two reasons: first, it is clear that the scale of resources devoted to price collection is much greater in the US. Second, and as one of the consequences of a lower level of resources, the CSO is extremely dependent on compliance and co-operation from firms, who it cannot effectively monitor. First of all, firms pick the products on which they are to report. Second, it is firms who have the responsibility of reporting changes in specification. Unlike the US practice, the CSO neither draws up specifications nor (usually) visits firms to check on compliance.

Some further checks within both the RPI and the PPI are possible. In both indexes, the number of occasions on which substitutions were made could be analysed more systematically. Substitutions occur when the specification of an item changes or when a model ceases to be available for pricing and an alternative item is priced instead. Substitutions affect the index in one of two ways, depending on whether they are assumed to involve no change in quality or a quality change equal to the difference in price between the old and the new item (or a combination of the two). The distribution by sector of the number of these two types of substitutions could be analysed as well as the trend over time. As most people seem to think that quality change is more important for durable goods, it would be interesting to see whether this view is supported by the pattern of the second type of substitution.

6. New Goods

The importance of new goods

The preceding section has discussed how allowance should be made for rising quality levels such as has occurred in mainframe computers and PCs. These two products also illustrate the problem of new goods. The rapid rise of the PC and the relative decline of the mainframe is presumably because consumers in general find that PCs reduce the overall cost of computation. But this fall in the price of computation is not captured by any conventional price index, hedonic or other. Typically, when a new good appears, there is a lag before changes in its price are incorporated into price indexes. After incorporation, changes in its price become increasingly influential as the proportion of expenditure devoted to it rises: the price index for computational devices is increasingly dominated by the price of PCs. But at no time is the fact that this new product is in most cases a superior substitute for pre-existing devices registered by the index.

It is a commonplace that economic growth has been accompanied historically by the appearance of new industries producing a profusion of new products (TV, radio, cars, X-Rays, computers) and by the disappearance or near disappearance of obsolete products (live bear-baiting, horse-drawn carriages, bleeding equipment and the abacus). Though in principle the number and variety of products on offer might fall during the process of growth, casual observation suggests the opposite: older products decline in importance but usually do not disappear altogether. For example, if one thinks of the technology for sending messages, postal and courier services still flourish, albeit with a lower market share, despite the successive advent of telegraphy, the telephone, radio, telex, fax, electronic mail, and tele-conferencing. On a shorter time-scale, the number of package tour destinations offered by a high street travel agent has undoubtedly increased in the last 30 years: the Costa Brava is still on offer, but so now is North America and the Far East. According to Baily and Gordon (1988), the number of lines displayed on US supermarket shelves has risen substantially in recent years.

If the variety of products is increasing over time, there is an obvious sense in which the purchaser (including the purchaser of investment goods as well as the purchaser of consumer goods) is better off. But the typical price index will not reflect this fact. The usual way in which a new product is incorporated into a real life price index is as follows. After the advent of a new product is noted (which may be some while after its actual appearance), changes in its price are weighted together with changes in the prices of other goods recorded in the index. Consider a highly simplified example: suppose each household takes one 2-week holiday a year, suppose the price of every holiday offered by the travel agent never changes, but the number of destinations on offer rises over time. A conventional price index, even one which included the prices of all holidays on offer (incorporating each new destination into the index as it became available), would show no change. But the real value of travel services offered and consumed has clearly risen - holiday makers don't have to go to Torremolinos every year unless they want to.

The identical argument applies to business services or to capital goods (Feenstra and Markusen, 1992). If the number of ways in which messages can be sent is rising over time, then clearly the purchaser of such services is better off, since he can choose the technology which is [TABULAR DATA OMITTED] best suited to the current need, and this improvement in service should be reflected in the measurement of the output of the communications industries. Equally, the computer purchaser is better off nowadays than at the dawn of the computer age, since he can choose that combination of micros, workstations, mini-computers, mainframes and supercomputers which best suits his requirements.(14)

Some of the recent 'new growth theory' literature suggests that the introduction of new goods may be an essential part of the story, for at least two reasons. First, the growth of total factor productivity may be due to the introduction of ever more specialised intermediate and capital goods (Ethier 1982; Romer 1987; Grossman and Helpman 1991, chapter 3). Second, unless new consumer goods become available, the growth of per capita output might cease, with the fruits of technical progress being taken in the form of additional leisure rather than additional production (Oulton 1993).

The reservation price approach

It seems that if we are ever to understand the process of economic growth, we must have some confidence that we have measured it reasonably accurately. In fact, economic theory has long known how to cope with new goods (or vanished old goods) in calculating a price index. In the case of a new consumer good or a new input, we should treat it as if it had always existed but at a price which just reduced demand for it to zero, that is, its reservation price. More precisely, the reservation price is the minimum price which just reduces demand to zero. Prior to its actual appearance, the new good's reservation price should be included in the index, and the good's actual price should be included after its appearance (Hicks, 1940). This makes it clear why ignoring new goods leads to an overestimation of price rises and a consequent underestimation of real growth. For the price of the new good has in fact fallen, from its reservation level to its observed level, which is necessarily lower.(15)

A simple numerical example will illustrate the point, as well as the extent of the bias in conventional indexes. Suppose there are four time periods and two goods, one of which is new in period 2. Let prices and quantities be as follows:

In period 0, the (unobserved) reservation price of good 2 is assumed to be 4. All other prices and quantities are observable. The new good accounts for about 9 per cent of total expenditure from period 1 onwards. The new good is assumed to be incorporated into the Laspeyres index as soon as it appears. The chained Laspeyres index (comparable to the RPI) is unchanged between periods 0 and 1, since it only reflects the price of good 1 which is constant. Comparing periods 1 and 2, it falls as the influence of the falling price of good 2 starts to be felt. By contrast the Tornqvist index reflects the notional fall in the price of good 2 between periods 0 and 1 as well as the actual fall between periods 1 and 2. Consequently, this index falls in both periods. Relative to period 0, the Tornqvist index has fallen in period 2 by 6.11 per cent while the Laspeyres has only fallen by 4.55 per cent.

If there is a lag before the new good is incorporated into the price index, the overestimation of inflation will be that much the greater. For example suppose that the new good is only incorporated into the Laspeyres index in period 2 and that from then on its price, like that of good 1, is constant. Then the Laspeyres index will show no fall in price at all in period 1, 2 or subsequently: the new good will appear not to have led to any reduction in prices at all.

The general situation is depicted in figure 1, which assumes that the price of the new good falls rapidly after its initial introduction at time [t.sub.1] until [t.sub.2], after which its price rises at the same rate as that of the other good. The reservation price, which is higher than the price at which the good is first sold, is shown by the dotted line. A conventional index should be able to take into account the fall in the price of the new good between [t.sub.1] and [t.sub.2] but if there is any lag in incorporating the good into the index inflation will be over-estimated. If the price of the new good is not in practice observed till [t.sub.2] or later, then the whole effect of the new good on inflation will be missed. Even if the price of the new good is observed from the moment of introduction at [t.sub.1], the notional fall in price which occurs at this date is not allowed for by the conventional index.

Use of the reservation price method has in practice been rare because of the difficulty of calculating the reservation price.(16) However recent results of Feenstra (1994) offer a hope that a practical way of implementing the approach may become possible. Feenstra shows that when the utility function takes the CES form, the true price index between two dates can be obtained from the crude one (which simply ignores the arrival of new goods or the disappearance of old ones) by multiplying the crude index by an adjustment factor, the latter dependent on a single parameter, the elasticity of substitution between products in the index. Grilches and Cockburn (1994) have employed econometric methods (including Feenstra's approach) to estimate reservation prices in the context of integrating the prices of generic drugs into pharmaceutical price indexes. However, for the moment these methods must be regarded as experimental.

The problem of new goods may be mitigated by the tendency for them to be introduced at a very high price which subsequently falls. In a favourable case, the first observed price might approximate the reservation price. This emphasises the importance of the prompt inclusion of new products into price indexes and of not waiting till they become important items in expenditure. In this contest it is important to note that (as I am informed) the maximum lag before a new good was incorporated into the PPI might at one time have been as long as 7-8 years, though nowadays it is likely to be considerably shorter.(17) However one should also note a practical difficulty in the way of early incorporation of new goods. There are probably many expensive novelties which are introduced in the hope that they will eventually become mass market items but which fail and are later withdrawn.

How important is new goods bias in practice? Lebow, Roberts and Stockton (1992) calculate what they call an upper bound for the effect of omitting new goods from the US CPI. They assume that new goods are only important in the categories 'Household appliances', 'Lawn equipment and power tools', and 'Medical care commodities', which account for 2.41 per cent of total consumer expenditure. They then assume that the prices of these commodities are falling at 20 per cent per annum, which they regard as an extreme estimate. The overstatement of the CPI is therefore about 0.0241 x 20 per cent = 0.48 per cent per annum, a relatively low figure. However, this calculation should be regarded as a 'guesstimate' rather than a genuine upper bound. There is no reason to think that new goods are only important in such a small part of the economy. If we assumed that new goods are important for producers' and consumers' durable goods in general, about 15 per cent of GDP, then by the same logic the overstatement of the GDP deflator would be 3 per cent per annum (0.15 x 20 per cent). In any case, new goods may appear in any sector and there is no hard evidence as to their actual rate of introduction nor as to the rate at which their prices typically fall.

7. Outlet Bias

Outlet bias may arise when the type of outlet through which goods are being sold is shifting over time. For example, consumers may be gradually shifting to a different type of store which offers the same product at a lower price. An example is the shift to large, suburban grocery stores away from corner shops and town centre self-service stores. The newer type may be of lower quality, though this is not necessarily the case, but this does not affect the main point that such shifts may not be fully reflected in price indexes.

As out-of-town supermarkets spread, and consumers vote with their feet (or their wheels) for this new product, the RPI will no doubt find an increasing proportion of its price quotations coming from the more successful type of store. However, the fact that in the eyes of most (though not all) consumers this represents a cheaper form of shopping is not reflected in the index. For example, the price of fruit may rise at the same rate in the two types of store, though the level is lower in large supermarkets. But with the new stores being linked on in the conventional way, the lower level of prices in supermarkets is not reflected in a conventional price index.

Reinsdorf (1993) has studied outlet bias in the US and suggests two tests of its extent.

(1) In the US the CPI uses a rolling sample of outlets in which 1/5 of the outlets are replaced each year. The implicit assumption is that there is no price dispersion as between outlets so that any differences in price for the same variety reflects outlet quality differences. So new outlets are linked on just as new varieties of for example, washing machines are. If this assumption does not hold and if replacement outlets on average have lower prices than existing ones, then there is outlet bias. He finds that this is in fact the case: for food, prices are on average 1.23 per cent lower in the new outlets, which suggests (ignoring quality differences in outlets) that the CPI is biased upwards by 0.25 per cent per annum. For gasoline, the corresponding figures are 1.29 per cent lower and 0.25 per cent per annum. The point is that new outlets are linked in like new products so that the shift to a cheaper alternative is not captured in the index.

(2) The BLS produces average price (AP) indexes for narrowly defined varieties, which are simply averages of all price quotes for the item. The implicit assumption here is that there are no quality differences as between outlets, the polar opposite of the CPI assumption. These indexes can be compared with the corresponding broader item in the CPI (for example, 'Eggs, grade A, large' is compared with 'Eggs'). For 52 food items, the CPI grew on average by 4.2 per cent per annum from Jan 1980 to Jan 1989, but the AP indexes by only 2.1 per cent per annum, suggesting outlet bias of over 2 per cent per annum. For gasoline, the difference between the 2 types of index is about 1 per cent per annum.

These differences are very large. Would quality differences between types of shop wipe them out? In general, the answer is no. First, it is not clear that the cheaper outlets are necessarily of lower quality: they may be just better for many customers. In any case, consumers value the quality loss (if any) at less than the price saving.

In the United States there were pronounced shifts in retailing patterns in the course of the 1980s, for example, the Wal-Mart phenomenon and the growth of warehouse clubs. These trends have not as yet shown up with anything like the same strength in the UK. Because of planning controls, it may be that they never will. The principal trend apparent from the rather limited statistics available about retailing is the growth of multiple stores. In 1980 they held about 54 per cent of the market and by 1990 their share had risen to 61 per cent. Over the same period, the share of both small multiples and single outlets declined (see Table 1). The RPI takes account of changes in shopping patterns since prices are collected for two different types of shop, 'multiples' and 'independents', though this breakdown is rather crude, and the weights assigned to each shop type are revised annually.

As with the US CPI, the CSO's present practice amounts to assuming that any difference in price between shop types reflects quality differences in the retailing experience, rather than simply the fact that one type of shop is cheaper. In other words, at the 'item' level (for example, sliced bread in the South East) the CSO calculates a weighted average of the price relatives:

[Mathematical Expression Omitted]

where w are weights, p are prices, subscripts M and I indicate multiples and independents respectively and superscripts t and b indicate month t and the base month (January). Suppose that prices in the two types of store happen to be constant over time, but that prices in multiples are lower [Mathematical Expression Omitted], and that consumers are gradually shifting to multiples. Then the CSO type of index (chained Laspeyres) will be constant and will be unaffected by the changing weights, even though the sales-weighted average price of the item is falling over time.
Table 1. Shares in retail turnover by type of shop, 1980 and 1990


 per cent


 1980 1990


Single outlets 32.2 26.9
Small multiples 14.3 11.7
Large multiples 53.5 61.4


Total 100.0 100.0


Source: CSO (1993b, Appendix A).


It would presumably be fairly easy for the CSO to recalculate the RPI on the basis of the alternative assumption, that none of the difference in price reflects quality differences as between shop types, as a test of the importance of outlet bias. Since shifts in UK shopping patterns are probably less pronounced, the effect on the index will probably be lower than Reinsdorf found.

Outlet bias can also be regarded as a new good problem, if we think of a given product being sold in one type of store as a different good from the same product sold in a different type. The opening of a new store is then like the introduction of a new good, except that it is only available to consumers in its own catchment area. In principle, the methods discussed above could be employed here too. But given that in the near future index numbers are unlikely to allow for the more standard type of new good, it might seem inconsistent to attempt to allow for outlet bias in this way.

8. How Well Do UK Price Indexes Cover The Economy?

There are a number of areas in which the coverage of price indexes is currently deficient. From the point of view of economic analysis, deflators are required to cover the whole economy. From the output side, PPIs were until recently confined to the part of the economy covered by the Census of Production (mining, energy and water, manufacturing, and construction) which has been shrinking and constituted only about 35 per cent of GDP in 1990.(18) Agriculture is also well covered but constitutes less than 2 per cent of GDP. In a new development, prices have just started being collected from 5 service industries: bus and coach hire, contract cleaning, private education, road haulage, and waste disposal (CSO 1993a). There are plans to produce indexes in the near future for courier, security and computer services, and for consulting engineering. Apart from these, no official price indexes are published for the output of the service sectors, which constitute about 63 per cent of GDP or 47 per cent if we exclude services which are predominantly publicly provided such as public administration and defence, health and education. Output at current prices and volume indexes are published for three broad sectors in services: wholesale and retail trade; transport and communication; and finance, insurance and real estate. In these sectors, real output indexes are based mainly on quantity indicators and sometimes even on employment (CSO 1985, pp. 41-44). The lack of official price indexes for services means that the study of output and productivity growth and indeed economic behaviour in general in more than half of the economy is seriously hampered.(19)

From the side of expenditure the picture is rather brighter. The RPI covers nearly all consumer expenditure on both goods and services, which constitutes some 64 per cent of GDP at market prices. The remaining broad categories of expenditure together with their 1992 shares in GDP are general government final consumption (22 per cent), investment (15 per cent), exports (23 per cent), and imports (-25 per cent). Investment expenditure is reasonably well covered by PPIs. Price indexes for exports and imports are based on unit value indexes, which have well known weaknesses.(20) There are no price indexes for government expenditure; volume measures are based on the convention that productivity growth is zero in this sector.

In summary, coverage of the economy by price indexes is far from complete, though better for expenditure than for output. On the output side, the main deficiency is the absence of indexes for services. As Griliches (1994) has pointed out, in some sense our knowledge of what is really happening in the economy may be deteriorating, due to the ever-rising importance of services.

9. Concluding Comments

Main findings

Allowance for quality change. In principle, the methods currently adopted in the UK to deal with quality change, which are similar to those used in the US, have no inherent bias, upwards or downwards. However, the findings of Gordon (1990), which constitute a large-scale replication of BLS methods on independent (and publicly available) data, suggest that in practice these methods make inadequate allowance for quality change, at least for durables (to which his study was confined). This implies that UK indexes may suffer from similar biases. If so, the problem is likely to be more serious with the PPI than with the RPI, for several reasons. First, resources devoted to the RPI are greater. Second, the PPI is very dependent on accurate compliance with instructions on the part of firms, who after all have little incentive to do more than the minimum now legally required.

If a bias of similar size to the one found by Gordon for the US exists also for UK durable goods indexes, while non-durable goods indexes are substantially correct, then overall the growth of the UK GDP deflator would be over-estimated by somewhat less than 0.5 per cent per annum. On the same basis, since consumer durables are about 14 per cent of UK consumer expenditure, the RPI would be over-estimated by 0.2 per cent per annum.

Gordon's findings suggest that in the US case, the failure was an administrative, not a methodological one. It is not entirely clear where exactly the failure lay. It seems likely though that on the PPI side, obsolete and unrepresentative products were retained too long in the index, and inadequate care was taken to ensure that changes in specification were noted. The main problem seems to have been the absence of independent checks on the validity of the indexes (see below). In the case of the PPI, confidentiality requirements hamper independent checking.

Substitution bias. If consumer prices are meant to measure the cost of living then base-weighted indexes will be biased upwards. But since the RPI weights are changed every year in the UK, this is probably not an important problem. Its importance could be easily checked quantitatively by, as an exercise, recalculating the RPI using a chained Tornqvist or Fisher Ideal index and comparing the result with the official index.

Outlet bias. Outlet bias seems to have been important in the United States, but so far is probably less important in the UK since retailing patterns have changed less. Present UK procedures assume that differences in price between shop types are entirely due to differences in the quality of the retail experience. The sensitivity of the index to this assumption could be tested by, as an exercise, recalculating the RPI (or components of it) on the opposite assumption, namely that price differences simply represent better value for money.

New goods. The introduction of a new good is conceptually equivalent to a fall in price, an effect which existing indexes (either here or abroad) do not allow for. Since the continuous introduction of new goods and increasing variety is a striking feature of the growth process, existing indexes are biased upwards. In principle, new goods can be incorporated into indexes using reservation prices, but at the moment there is no practical way of implementing this method in general. However, the impact of the omission of the new goods effect is mitigated if new goods are incorporated as early as possible into price indexes, since it seems likely that (at least for durables) large price falls occur in the early stages of the product life cycle.

Coverage of the economy by price indexes. Coverage is better on the expenditure side than on the output side. Consumers' expenditure, nearly all of which is covered by the RPI, accounts for 64 per cent of GDP. But price indexes for exports and imports (each about a quarter of GDP) are of poor quality. On the output side, the part of the economy covered by the PPI is shrinking in importance and currently accounts for only about 35 per cent of GDP. The service sector constitutes nearly two thirds of GDP (nearly half even excluding publicly provided services) and yet is almost entirely uncovered by price indexes on the output side.

As mentioned in the Introduction, it is commonly held that price indexes overstate inflation, perhaps by as much as 2 per cent per annum. We have not found any hard evidence to support so extreme a view. On the other hand, most of the possible biases seem to be towards overstatement of inflation. However, in crucial areas the evidence necessary to quantify the size of the biases is lacking. In some cases, as with substitution bias or outlet bias, we can be reasonably sure that the bias is fairly small. In other cases, as with new goods, there is really no way of assessing, in the present state of knowledge, how large the bias is. There seems little point in trying to guess the size when the basis for an estimate does not exist. In the physical sciences, if some unknown quantity is thought important enough, resources are devoted to measuring it, rather than effort wasted in guesswork. If measuring inflation or real output growth to within, say, one decimal point is considered important, then the same approach should be adopted.(21)

NOTES

(1) This note summarises the results of research financed by HM Treasury. A fuller version is Oulton (1995). I am grateful to a number of officials of the Treasury and of the CSO, and also to my colleague Ray Barrell, for discussions and advice. The conclusions are however my own and should not be thought necessarily to represent the views of the Treasury, the CSO or any of its officials.

(2) Crawford (1993) considers the lower figure is a reasonable upper limit for the Canadian Consumer Price Index. Lebow et al. (1992) suggest that the comparable figure for the US Consumer Price Index is 1.8 per cent per annum, while Wynne and Sigalia (1994) believe 1 per cent per annum to be more reasonable. Alan Greenspan, Chairman of the Federal Reserve, has recently suggested that the US CPI overstates inflation by as much as 1.5 per cent per annum (The Economist, 28 January 1995, p. 48). Briscoe and Reckless (1994) suggest that the Retail Price Index is overstated by 2 per cent per annum or more.

(3) There is an analogous definition of the price index for inputs into production which runs in terms of production isoquants rather than indifference curves. The theory of the output price index is developed in Fisher and Shell (1972, Essay II). A textbook exposition of the theory of COL indexes is in Deaton and Muellbauer (1980, chapter 7). A more elaborate account is Diewert (1983). A succinct discussion of index number theory in general is Diewert (1987). Turvey et al. (1989) is a manual for practitioners.

(4) There is no current official handbook describing the methodology of the RPI, comparable to the one describing the PPI (CSO 1980). The methodology and philosophy of the RPI is discussed in general terms in Retail Prices Index Advisory Committee [RPIAC] (1986). The National Audit Office (1990) report on the RPI describes the administrative process involved in an illuminating way, at least as it was prior to the transfer of responsibility from the Department of Employment to the CSO. An unpublished internal memorandum which I have been shown gives more details of current procedures. The following brief description draws on these sources.

(5) Microwave ovens were added to the Canadian CPI in 1983 but by January 1985 had a weight of only 0.06 per cent (Crawford 1993). The market penetration of these products may well have been more rapid in Canada than in Britain.

(6) The methodology for constructing PPIs is described in CSO (1980). Some further practical features of the process of constructing the indexes are in CSO (1993a). A discussion of recent changes in the process and a comparison with foreign methods is Walker and Richards (1992). Some useful details of current procedures are in the recent review of the PPI (CSO 1993a).

(7) Price increases of more than 5 per cent are queried as are all price falls (except where these have often occurred in the past). Items whose price has not changed for the past 18 months or more are also queried (CSO 1993a, p. 7).

(8) This skips over some technicalities, see above.

(9) A Laspeyres index is usually but not invariably found to show a larger price rise than a current weighted (Paasche) index. This is a different point to the one in the text.

(10) Sainsbury (1994) argues that the quality of red meat fell significantly after the 1960s and then subsequently recovered.

(11) More realistically, age and model dummies should be introduced as well and these raise a number of subtle issues as to how the quality-adjusted rate of inflation should be measured (Berndt et al. 1993).

(12) An interesting comparison of the traditional matched models and the hedonic approaches has been made for apparel by Liegey (1994). He finds no consistent tendency for hedonic methods to produce either higher or lower rates of price change.

(13) The methods currently used by the BLS for their producer price index are described in US Department of Labor (1992). It is clear that there was a considerable upgrading in their methods starting around 1978 and continuing till at least 1986. But this upgrading has only affected the indexes for the years since 1978, so for our purposes earlier methods are still relevant. The BLS method of adjustment for quality change, at least as it was in the 1970s, has been described by Early and Sinclair (1983). Their account can be supplemented by Gordon (1990, chapter 3).

(14) The purchaser of a mainframe is also better off because the typical mainframe today is faster and has a larger memory than did its counterpart of the 1950s. But this type of improvement is quite different from the benefit which derives from greater variety.

(15) In the case of a new good appearing in an output price index, the correct price to use prior to its actual appearance is the maximum price which would just reduce supply to zero.

(16) Gordon (1990, p.36) reports that the first videotape recorder sold for $75,000 in 1956; the first Betamax home videotape recorder (without remote control or programming capability) sold for $2,295 in 1975. However, the opposite pattern also occurs: some products are initially offered at low prices in order to get established in the market, but their prices subsequently rise if they prove successful: an example is Australian wine in the UK market.

(17) The new PRODCOM system is expected to help speed up the recruitment of new goods into the PPI. Of course, historical series of the PPI will continue to reflect the earlier, longer lag.

(18) Despite the availability of PPIs for the production sector, they are not necessarily used to produce the official constant price estimates of output. In fact, there is a surprisingly high proportion of output in this sector, 38 per cent according to CSO (1985, p. 43), for which constant price estimates are still produced using quantity indicators, not PPIs.

(19) O'Mahony (1994) reviews the procedures for measuring real output in service industries in more detail. See also Armknecht and Ginsburg (1992), Dean and Kunze (1992) and Mohr (1992) for US experience.

(20) The UK is rather unusual in that PPIs only cover home sales, not exports (Walker and Richards 1992). However, there are proposals to extend the PPI inquiry and gather export prices directly (CSO 1993a, p. 19)and this process has now begun.

(21) See Oulton (1995) for a range of suggestions for further research. These range from simple and relatively cheap consistency checks to more expensive, longer-term proposals.

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