sou · GNB3124 · 2000-01-01 00:00:00 — This last property is an advantage for example for central banks that want to monitor inflation by looking at how series of 12-month changes develop.6 In a chain index, on the other hand, the 12-month change will usually be between two consecutive index links so that there is a weight change in between. This weight change is an unwanted disturbance and, at the turn of each year, there will be a break in the time series so that the change in the 12-month rate when going from to January will be only partly due to real price changes and partly to weight changes and other technical adjustments to the index. (A chain index based on linking only short-term according to (6) would not have this problem.) On the other hand, but perhaps less importantly for inflation analysts, the estimates will be unbiased on average. The sizes of these disturbances have been simulated. We do not present these simulations in detail here but on average the absolute sizes of these differences are around 0.1 for all the major chain index alternatives discussed here, except the one with only short-term . At the maximum, the annual jumps can be as large as 0.4. 6 On the other hand, in the end of every link it will eventually be possible to recalculate these changes based on the new weights. This creates a situation where inflation history will be rewritten which can also create problems. delayed chain index, the jumps are the largest but the differences are not great. It is only meaningful to look at axiomatics within each index link. The basic index tests (see Bilaga 2 for their definition) – monotonicity, identity, proportionality and dimensional invariance – are satisfied by all formulae considered here. The time reversal test is satisfied by all superlative formulae (and ) but not the base period weighted formulae. We consider this test important, since it guarantees some kind of symmetry between the periods compared that indicates unbiasedness. The factor reversal test is only satisfied by index. This test is not crucial for a CPI, for which a dual volume index is not directly asked for. The geometric , including , break down for zero prices, which the other can manage. This property has some importance, since prices for some public services sometimes change from/to zero. Consistency in aggregation is only satisfied by the base period weighted formulae, not by the superlative . However, we believe that this test is too strong to be of importance. A weaker additivity criterion is discussed below under the heading easy to analyse. Diewert (1999) recently proposed a test, which distinguishes the index, which does not satisfy it, from the other , which do satisfy it. He calls this the invariance to proportional changes in current quantities test with the following definition:7 P(p0,p1,q0,lq1) = P(p0,p1,q0,q1) for all p0,p1,q0,q1 and all l>0 (41) 7 There is a potential problem with the use of the price index that has been noticed in the context of using the formula to make international comparisons of prices. If the price levels of a very large country are compared to the price levels of a small country using formula then the quantity vector of the large country may totally overwhelm the influence of the quantity vector corresponding to the small country.7 In technical terms, the formula is not homogeneous of degree 0 in the components of both q0 and q1. To prevent this problem from occurring (we ask that the price index) satisfy the following invariance to proportional changes in current quantities test This test is more relevant in a spatial comparison between two countries of different sizes. In a temporal comparison, especially between two consecutive years, the quantity vectors are sufficiently close for this problem not to be significant. In summary, we consider the , and to satisfy the important criteria, with a slight disadvantage for . 4.6.4Correct handling of seasonal products This criterion speaks strongly for a year base period and against the present system with month base periods. The criterion does not distinguish between formulae, since these could all, with some difficulty, be adapted to take care of seasonal products. have some problems with the first monthly index in a new link because of the introduction of new weights in that index which takes extra time and causes a delay. In a fixed base index, one simply continues with the old weights until the new are finalised and thus solves the problem. In the delayed chain index it should be possible to avoid the annual delays, since there will be more time for the weight preparations. 4.6.6Easy to interpret and analyse Neither the , nor the geometric or can easily be looked at as monitoring the cost for a fixed basket of products. They cannot either be written in the established algebraic form of a sum of weights times subindices, which the producers and analysts are used to handle. This is a considerable disadvantage for such a broadly used, popular index as the CPI. However, both the and the index (like the Laspeyres index) possess these important properties, since they are defined as the ratio of the costs for two baskets with the quantities being averages of those of the base and the comparison period. Thereby, they also possess a simple additivity property, in the sense that weights for subindices can simply be added to obtain weights for higher aggregates. This criterion can be seen as a weaker form of the consistency in aggregation test and we believe that it covers what is needed for practical CPI purposes. All our proposals in this report satisfy non-revisability by design. If this criterion were not crucial, various other possibilities would exist which could lead to greater reliability in both long and short term comparisons. Such solutions would probably also add to the complexity of the system, however. 4.6.8Co-ordination with the HICP The HICP is defined as a Laspeyres-type index with a year as the index reference period. At the same time, there is a requirement to update weights and introduce new products annually, if such measures are important for comparability. None of the solutions discussed in this report fully satisfies HICP requirements. However, the additional work for adapting a KPI system to the HICP requirements are not judged to introduce any new problems compared with today. Changing over to a new aggregation system of course leads to a one time extra cost. It is outside the scope of this report to estimate this cost. The current costs for running the systems are lowest for a fixed base system but it depends on the ambition, when it comes to introducing new products and outlets at the lower level of the index. The cost for having a year as a base period is probably somewhat higher, since the calculation systems at lower levels will involve more links and longer time spans (see below). The difference is not believed to be large, however. With the criterion minimal long-term bias in relation to a cost-of-living index/superlative index as our main criterion, the above evaluation clearly boils down to a recommendation to choose a delayed chain index according to equation (20). This choice immediately makes a superlative index aggregation over some 90 product groups possible and, with better National Accounts and other sources for weights, it opens for extending superlative aggregation to much finer levels of the index. For the year-to-year links in this index, all superlative formulae (including ) are virtually equivalent from a bias point of view. The criterion easy to interpret and analyse points at or as the clearly best choices. A small edge is given in favour of , due to its true superlative properties and meeting more tests. For the year-to-month link, simplicity speaks in favour of the Laspeyres index. Its bias does not influence the long-term bias of the chain index as a whole. 5 Index aggregation at lower levels The analysis above has led us to recommend the following basic KPI construction. The index from reference year 0 to year Y, month m should be a chained index according to the following formula: = IY - 2 Õ I y - 1 For the year-to-year index, the index should be used: å Pky Qky Qky - 1 = å Wk ;W å Pky - 1 Qky Qky - 1 where Wk ;W = For the year-to-month index, the Laspeyres index should be used: P Y ,m = å W k , where W k This computational scheme will be possible to use down to at least 90 product groups for which consumption values from the National Accounts will be available. Work is going on to extend this breakdown further down the product hierarchy. In this section, we will deal with the problems that emerge below the level, where these value weights are available. For the purposes of the present analysis, it is useful to speak of four aggregation steps. In actual index calculation, there may sometimes be more or (less often) fewer steps than that but they can then be traced back to one of these four steps. We will, somewhat unnaturally number them from top to bottom. We will give examples of the kind of situations that we have in mind as we go along. The first step – the combination of some 90 NA purposes into the All Item Index In this step, current NA value weights are guaranteed in our proposed system. The purposes are according to the international Coicop (Classification Of Individual Consumption by Purpose) system and are similar to those used in the HICP. The second step – the combination of 3–400 product groups into 90 NA purposes In this step NA values are also possible but not guaranteed and we have to prepare for some less than superlative aggregation method as the best estimate. Aggregation is in this case over products within the same product group. In some cases, these are fairly close substitutes such as pork and beef within the meat category. In other cases, substitutability is much smaller such as between dishwashers and refrigerators in the household appliances category. The third step – combining elementary aggregates into product groups This step is quite heterogeneous in nature. In most cases value weights will not be available, although exceptions exist. In the third step product groups subindices are constructed, sometimes in several steps, from subgroup, outlet and/or regional elementary aggregates. For this step, there is a great variety of situations. A few examples are given here. Local price collection. For some 150 representative products (mainly goods), local price collectors monitor the prices directly in the outlets. For these products there is a stratification into industries (outlet types) according to SNI 92 (the Swedish version of the NACE system for industrial classification). (Elementary aggregation is done nationally, over all outlets in one industry.) Weights over industries are based on a survey planned to be 5-yearly, reflecting the distribution of sales of a certain product group between industries. The daily necessities system introduces an additional stratification compared with the local price system. Here, e.g., the industry Supermarkets (SNI 52.112) is further divided into three strata according to the chain a certain outlet belongs to (ICA/KF/). In this subsystem aggregation is over the following dimensions: i) Network fees vs. energy fees, ii) type of housing, iii) fixed vs. variable (=according to consumed amount) fees and iv) type of tariff used (partly according to the consumers choice). Municipal services for owner-occupiers. Here, aggregation is over i) type of service (water and sewage, refuse collection and chimney sweeping) and ii) municipalities. Aggregation is over i) main type of services (mobile services, residential services, and Internet services), ii) company providing the service and iii) detailed services according to the tariff of the provider. Aggregation is over i) type of service and ii) organisation providing the service, where the organisation is usually a county council (landsting) so that there is also a geographical division involved in this aggregation step. We observe that the third level displays a very mixed picture with regard to substitutability. The subgroups sometimes represent entities between which substitutability is large (e.g. outlet chains) and sometimes very small (e.g. municipality of ). The fourth step – aggregating price quotes into elementary At this level, single observed prices are aggregated to elementary . In practice, there are several different cases here. Fairly typical examples in the KPI are: 1.A representative item (e.g. a refrigerator, a TV set, a restaurant meal) is defined in the central office. Varieties of this item are selected by price collectors and are thus aggregated over a certain type of randomly (PPS)8 selected outlets (5-digit NACE number) in all of . The available weight information is the size of the outlet in terms of its number of employees (with a 2-year lag). 8 Probability Proportional to Size 2.For most item groups in daily necessities (e.g. bread, cereals, frozen fish, washing detergents etc.), typically purchased in supermarkets, randomly (PPS) selected items (e.g. cod fillet, Findus, ) are aggregated over randomly (PPS) selected outlets, divided into three major wholesaler/retailer chains, in all of . In addition to the size of the outlet, the weight of the item in terms of its national sales 1–2 years ago is known. 3.Water and sewage charges are aggregated over a number of randomly selected municipalities. The population size of the municipality is used as weight. 4.Complete information of the sales of all alcoholic beverages by the Government retail monopoly (Systembolaget) which uses national prices. The exact quantities/values sold of each bottle/can of beer, wine or spirit are known. 5.Electricity or telephone charges are aggregated over a number of providers. Usually, good information on quantities (kWh, call minutes etc.), although sometimes with a lag, is available. As a rule, substitutability within the aggregates will be large.9 Sometimes there are also weights involved at this level, sometimes not. In some cases such as tariff prices in item 5 of the list, there are specific problems, which will not be dealt with here. 5.2Estimates of price elasticity For determining the best aggregation method in the absence of current value weights, we will use the price elasticity criterion. We will assume that the relation between price elasticity and index formula is given by the CES price index in (16) above. With this formula in mind, the empirical issue becomes one of determining the value of the price elasticity s in different cases. Unfortunately, the available information is not abundant. Most estimates are done in the U.S., only one recent Swedish source is known. We will first look at these estimates at a level roughly corresponding to the second aggregation step. Then we will look at evidence relating to the third and fourth steps. 9 Although an aggregate often covers the whole country, price changes do not usually follow a regional pattern. This means that the observed variation within an aggregate often represents variation between nearby outlets. The only recent Scandinavian source for price elasticities is Edgerton et al. (1996). They analyse food demand in the Nordic countries based on NA data from 1963–89 for and similar time periods for the other Nordic countries. They use a three-level aggregation, where food consumption is divided into animalia, vegetabilia, beverages and miscellaneous and each of these categories is in turn divided into three subgroups, the lowest level considered in their study. Table 6 gives their estimated own-price elasticities for each of the 12 groups: Table 6: Own-price elasticities (reversed sign) for the Nordic countries, estimated by Edgerton et al (1996) Milk, cheese and eggs The groups in Table 6 are, however, groups, that belong to the upper level of KPI aggregation, where current consumption values are available, at least in principle.10 10 At present, the NA values for these food categories are not based on current information but are just extrapolated from earlier years in fixed value proportions. It will, however, be possible to improve these matters with some reasonable effort. McLelland (1999), at the U.S. (), makes detailed comparisons between outcomes of different index formulae within the expenditure class level of the U.S. CPI (70 groups divided into 207 item strata). In the KPI, this level roughly corresponds to the division into 300 subindices mentioned above. He finds that the estimated elasticity of substitution is close to or greater than unity in the majority of cases. In comparing the , Laspeyres and Geometric he finds that Laspeyres is significantly different from the in 65 to 80 percent of the cases, whereas the Geometric index (with old weights) only differs significantly in about 15 percent of the cases. Thus the Geometric index is judged to be a better estimator of a cost-of-living index than the Laspeyres, when only old weights (from period 0) are available. McLellands main objective is to establish the best methodology at the elementary index level. He argues that, due to increased substitution at the lower levels of the index, the elasticity generally increases as we move down in the index hierarchy. This causes the differential biases of the Laspeyres and the Geometric in relation to to move further in favour of the Geometric index. A survey of published estimates of demand elasticity in the U.S. shows a somewhat mixed picture. Three important recent works in this area are (1993), , Levinsohn and Pakes (1995) and Hausman (1997). is concerned with the food sector. He estimates the elasticity of food at home as a whole to be 0.19 but as the level of disaggregation increases the elasticity also generally increases, although with some exceptions. In table 7, we present a summary of his estimates. Table 7: Price elasticities (reversed sign) in some food categories for the U.S. according to (1993) Subgroups of meat and fish , rice, eggs, milk and cheese Subgroups of fresh vegetables Subgroups of processed fruit and vegetables Subgroups of sugar and fats The difficulties in this area are underlined by some very different estimates by other researchers; (1994) estimates elasticity for milk to 1.15 and Heien and Pompelli (1989) to 0.69. Unpublished Swedish experiences from the recent period when milk subsidies were abolished and prices thus suddenly increased by some were that purchasing volumes were influenced at all, a fact that supports the low elasticity estimates for milk. Hausman gives 0.90 as his estimate for breakfast cereals as a whole. For cars as a whole, three estimates are 0.87 (, 1996) 0.85 (Levinsohn, 1988) and 1.43 (Trandel, 1991). The great variability of the elasticity estimates, also for the same product groups, precludes strong conclusions for any particular group. The estimates cover the whole range from slightly above zero up to values above one and thus make a definite judgement on average price elasticity difficult. We consider McLelland's results as the single strongest evidence relating to the formula choice at this level, since he compared index formulas with their superlative counterparts afterwards and with actual CPI data. His conclusion is that the estimated elasticity of substitution is close to or greater than unity in the majority of cases and thus that the geometric mean estimator, which is based on an assumption of price elasticity being equal to one, estimates a superlative index better than a Laspeyres index does. With Table 7 in mind, it may be possible to make informed guesses as to categories where an assumption of unitary price elasticity is not reasonable and apply different aggregation principles in the two cases. Let us first ask: What is the economic interpretation of an elementary aggregate (EA) and of the kind of consumer behaviour that takes place within it? For food, daily necessities and some other products, the EA in the KPI consists of a set of varieties in a set of outlets defined either as a chain of retailers or as an outlet type (example hypermarkets, radio/TV- retailers etc.) defined by the 5-digit NACE level (SNI 92, the Swedish NACE version). In contrast to most other countries, no regional demarcations are applied. How, then, do consumers behave in response to price changes within such an EA? Firstly, we note that much of the low-level substitution would take place also between two EAs, for example between a hypermarket and a local supermarket or between a and an ICA supermarket in the same area. This calls for a substitution allowing aggregation principle between different outlet groups for the same product. Within an EA, there will be substitution effects unless the price changes display a strong regional pattern. Regional effects are not strong, since much of the price change is known to be due to short-term fluctuations, price bouncing etc. Therefore, within an EA substitution effects are generally large. What substitution effects are we talking about more exactly at this level? et al (1998) made an excellent account of this when they explained the BLS change to the geometric mean formula at the EA level. Ice cream was used as their exemplifying product: Substitution can take several forms corresponding to the types of item- and outlet-specific prices used to construct the basic indexes: ·Substitution among brands of products, for example, between brands of ice cream; ·Substitution among product sizes, for example, between pint and quart packages of ice cream; ·Substitution among outlets, for example, between a brand of ice cream sold at two different stores; ·Substitution across time, for example, between purchasing ice cream during the first or second week of the month; ·Substitution among types of items within the category, for example, between ice cream and frozen yoghurt; ·Substitution among specific items in different index categories, for example, between ice cream and cupcakes. Thus, in response to an increase in the price charged by a store for a certain brand of ice cream, a consumer could respond by redistributing purchases along any of several dimensions represented by other priced items in the category: to another brand of ice cream whose prices had not risen, to a larger package of ice cream with a smaller price per ounce, to ice cream at a different store where ice cream is on sale, or to a brand of frozen yoghurt. The consumer also could respond by postponing the ice cream purchase until a later date. Finally, the consumer could substitute from the ice cream brand to a specific alternative dessert item, such as cupcakes or apples, that is in another CPI category. The distinctions between all the kinds of substitution elements described in this quotation are not well developed in economic research.11 What can be said under these circumstances? 11 A research line that is in its infancy is that of consumer search theory. Reinsdorf (1994) discusses the implications for the cost of living index of searching consumers in markets with price dispersion for products of quality. In general it is reasonable to expect elasticities to increase when we move down the product hierarchy to more detailed levels. This is because we find closer substitutes at the lower levels than at the higher (pork vs. beef instead of meat vs. fish, Brand A vs. Brand B coffee instead of coffee vs. tea, Coca Cola in outlet A vs. the nearby outlet B instead of Coca Cola vs. However, not many studies of low level elasticities have been done so far. et al estimates elasticity for cars and give estimates between 3.08 (Lexus LS400) and 6.52 () at the brand level as compared with the above-mentioned estimates for cars as a whole between 0.85 and 1.43. Hausman deals with breakfast cereals, also at the brand level.