The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
FEDERAL RESERVE BANK OF RICHMOND MONTHLY REVIEW MEASURING PRICE CHANGES Part Ttvo of a Three Part Series INTRODUCTION The first part of this article, which appeared in last month’s issue of this Review, discussed recent behavior of the major price indexes— the Consumer Price Index, the Wholesale Price Index, and the Implicit Price Deflator for GN P. These indexes and their components are closely watched by eco nomic analysts, and changes in them are extensively analyzed for evidence of progress or lack of progress in the effort to combat inflation. Increasing atten tion has been focused on the indexes during the recent highly inflationary period, and, as might be expected, the technical characteristics of the indexes have received added scrutiny. Since much depends upon the indexes in policy making, planning, and forecasting, it is appropriate to ask whether the in dexes are accurate, and whether the methods used in constructing them are statistically sound. This part of this article examines the conceptual and statistical problems encountered in the design and construction of price indexes. Its purpose is expository. Certain criteria for good indexes are discussed as well as certain problems associated with the interpretation of index numbers. The final part of the article, which will appear next month, will review the specific methodologies used by the D e partments of Commerce and Labor in the compilation of the major indexes in current use in this country and will evaluate those indexes in the light of the criteria discussed in this part. THE DESIGN AND CONSTRUCTION OF PRICE INDEXES An index in the simplest sense is a ratio of one quantity to another. It expresses a given quantity in terms of its relative value in comparison to a base quantity. Thus, a price index designed for the purpose of measuring price changes over time is a ratio of one price (or combination of prices) to the price of the same item (or combination of items) in a different period of time. When properly con structed. index numbers of prices permit the com parison of economic values over time net of the effect of price changes. Several conceptual and statistical issues involved in the development of meaningful and reliable price 2 indexes to represent the aggregate movement of prices over time are raised in the discussion which follows. For purposes of illustration of the concepts, a hypothetical example is used throughout the discus sion of a consumer whose total budget consists of five items, and whose expenditures on the items are shown for a period of four years. Three of the items are large in relation to his total budget— auto mobiles and suits, which are purchased infrequently, and rent, which is paid frequently. Tw o of the items are small, but one, bread, is purchased frequent ly, and the other, movie tickets, is purchased infre quently. The five items taken together comprise a theoretical “ market basket"— a term commonly used to refer to the sample of items upon which an index is based. Usually, the “ market basket” is a sample of selected items typical of the consumer’s purchases and is used to represent his total budget. In this simplified example, however, it is assumed that the five items comprise this consumer's total budget. Table 1 shows the consumer’s situation. This e x ample, though an oversimplification of the problems involved in constructing aggregate price indexes, illustrates a number of the issues. Conceptual Problems The Base Period A fundam ental problem in the development of index numbers is the selection of a base. If a price index is to serve as a stable basis for comparison of price movements over time, a period of time must be selected and held as the base long enough to generate a series of indexes for subsequent periods that will be useful in com paring those periods not only with the base, but with each other. Price indexes designed for analysis of price changes over time which are also computed for different places, such as the Consumer Price Index, do not automatically provide a valid basis of com parison of one place with another. Since the index relates current prices at a particular location to those in the base period at the same location, without regard to the standardization of base prices among the several locations, the index is useful only for comparisons over time. Current usage of price in dexes is generallv restricted to temporal comparisons Therefore, attention is devoted only to indexes designed for that purpose in the discussion which followrs. Where the object is to devise an aggregate index for general-purpose use, the selection of a base period is necessarily somewhat arbitrary. Under ideal conditions, however, the base period would be one in which extremely erratic movements are not oc curring in prices themselves or in underlying eco nomic conditions which would be reflected in prices. Such “ normal” periods are difficult to define where prices of hundreds of items must be taken into ac count. W here the index is more of the special- pur pose variety, the selection of an appropriate base is somewhat easier. For example, the earliest concern with index numbers involved an attempt to measure the change in the purchasing power of money (i.e., the reciprocal of the price index) resulting from the importation of silver into Europe after the discovery of America. This first price index, developed by Carli in 1764, covered a 250 year time span with later one for which the revised sample of goods and services is representative. Though it is sometimes desirable, it is not neces sary that both of the above changes be made at the same time. A n updating of the sample of goods and services can be accomplished without shifting the base if the revised selection of items is worked into the sample so as not to distort the continuity of the index. This type of adjustment is discussed later in connection with other statistical problems. A straightforward shift of the base period is possible, however, without changing the sample of goods and services if it is known that the original sample se lection remains valid, and if all that is desired is a revision of the index base to a more recent date. For example, if the index of 1970 prices for a par ticular sample of items on a 1960 base is 120.0, and the index on the same base was 105.0 in 1965, then 1970 prices can be expressed on a 1965 base as 114.3, or 120.0/105.0.2 This kind of linkage, while frequently used, does nothing to improve the quality of the index. The revised number gives the same information that the original index did, but expresses it in terms of a more recent base. The revision in no way allows for changes in quality of goods and services or changes in spending patterns which result from price changes. Thus, the crucial question to which an index must frequently be subjected is whether or not the sample of commodities is cur rently valid. If it is, no revisions of the base period or the sample are needed. On the other hand, if revisions of the sample are needed, a shift of the base period may be convenient, but not essential. the year 1500 as the base.1 Base periods of price indexes are occasionally up dated for convenience. A s spending patterns change and as technological change occurs, particular selec tions of goods and services comprising the “ market basket” become obsolete as standards for comparison. Items which are commonly purchased in a current period may not have been available in the base period or may have undergone substantial technical or quality changes since the base period. This re quires a revision of the sample, and this change may be accompanied by a shift of the base period to a 1 Mudgett, Bruce D. Index N um bers. N ew York, 1951. p. 6. John W iley ‘J It is common practice to express index numbers as ratios multiplied by 100 and rounded to one decimal place (e.g., the index 114.3 is the ratio 1 .1 4 3 ). It is understood throughout this article that a ratio obtained by any form ula is multiplied by 100 to obtain an index. For simplicity that step is not shown in the calculations or formulas. & Sons, Inc., Table I HYPOTHETICAL CONSUMER WITH A FIVE-ITEM "M ARKET BASKET7 Prices and Q uantities Purchased Item Y e ars 1 Autom obiles, each Rent, per month Bread, per loaf M ovie tickets, each Suits, each Total Expenditures Note: 2 Pi qi $ 2,0 00 .0 0 80.00 .20 .75 85.00 12 250 10 4 $ $ $ $ $ 3,357.50 i q •> $ 2,2 0 0 .0 0 85.00 .22 1.00 95.00 i 12 275 6 4 $ $ $ $ 4 3 P2 Ps q3 $ 2,5 00 .0 0 100.00 .25 1.25 115.00 0 12 275 10 3 $ $ $ $ $3,666. 50 $1,626. 25 Pi q4 $ 2,5 00 .0 0 130.00 .23 1.35 135.00 1 12 300 10 1 $ $ $ $ $ 4,2 77 .5 0 Subscripts represent y ears, an d p and q represent prices and quantities respectively. 3 Simple Average of Relatives and Simple Aggre gative Price Indexes T h e sim plest form of price index is the ratio of one price to another for a specified commodity. This approach is valid under extremely restricted circumstances. For example, consider the consumer whose expenditures are shown in Table I. Assuming that the loaf of bread listed in the table is the same loaf in size and quality in all four years, a simple index of the price of bread in year 2 is 110.0 (year 1= 100). For years 3 and 4, the index is 125.0 and 115.0, respectively. A s far as it goes, this index is a valid measure of changes in the price of bread. If no change in quality could be assumed for the other four items shown, similar price indexes could be constructed for them. But a serious problem arises, even in the absence of any quality changes, if a composite index of this consumer’s “ market basket” is desired. Consider, for example, only the change between years 1 and 2. The price index for bread, as previously stated, is 110.0; for automobiles, it is also 110.0; for rent, it is 106.3; for movie tickets, it is 133.3; and for suits, it is 111.8. A simple average of the individual indexes yields a composite index of 114.3 for this consumer’s total budget in year 2, based upon year 1. This index is questionable since it implicitly gives the highest weight among the five items to that one which rises most in price in percentage terms. That item is movie tickets, one which is of relatively little consequence to this con sumer. The index formula used in the above illustration is known as a simple average of relatives, or I i 2= S ( p 2/ p i ) / n , where I x 2 represents the value of the index for year 2 based upon year 1; px and p2 represent prices of individual items in years 1 and 2, respectively; 2 is the standard symbol for summation; and n is the number of items comprising the index.3 Other means of averaging the price relatives (or ratios) could easily be used. For example, a median of relatives (110.0 in this case) reduces the upward bias resulting from the increase in movie ticket prices. Other methods of averaging price indexes which are frequently employed in order to reduce upward bias resulting from a sharp rise in one item or component are geometric averages and harmonic averages. A comparison of all these procedures for the hypothetical consumer for the four years given is shown in Table II, and selected indexes are graphed in the accompanying chart. 3 Mills, Frederick C. Statistical M ethods. & Co., N ew Y ork, 1955. Ch. 13. 4 Third Edition. Henry Holt COM PARISON OF SELECTED SIMPLE AND W EIGHTED PRICE INDEXES FOR HYPOTHETICAL CONSUMER YEAR 1 = 1 0 0 For comparison, another type of index number construction which might be used is the simple ag gregative type. For the consumer under discussion, the total of the prices of the items he buys in the base period is $2,165.95. In year 2, the total of these prices is $2,381.22. A simple aggregative index number for year 2 is I, 2= 2 p 2/ 2 Pl= 1 09 .9. Whether this number is any better as a measure of the price changes affecting the consumer is still in question. This procedure implicitly gives the highest weight among the items to the one which has the largest price change in absolute terms. In year 2. that item is automobiles which increased $200. This index is thus highly dependent upon the units for which prices are quoted. Simple aggregative indexes are given for the four years in Table II and in the chart. The chart illustrates that this index has practically no increase in the fourth year when auto prices do not rise while the other indexes shown continue to climb. Both of these simple index methods raise questions of how to reduce biases in price indexes which arise due to large relative price changes (the movie ticket example) or large absolute price changes which may be small relative to the price of the item (the auto mobile example). W hile both of the simple indexes appear to be unweighted, they actually contain im plicit weights, due to either actual price changes or as prices, the resulting ratio is not a pure index of have changed at the same time as a result of changes in his income, changes in the quality of items which he purchased, and for numerous other reasons. One type of question which a price index is commonly expected to answer is how much it would cost the consumer in the current period to purchase exactly the same mix of items ( “ market basket” ) that he purchased in the base period, assuming no change in the quality and utility of the goods and services he selected. The latter assumption is difficult to allow for in the construction of indexes, but the desired answer to the question is at least approximated if the quantities purchased in the base period are chosen as weights and held constant in computing the index for subsequent periods. If such weights are used, the necessity for periodic updating of the “ market basket” is clear. As will be shown in subsequent discussion, however, not all indexes are designed to answer the specific question posed above. The type of index described above is of both the fixed-weight and fixed-base variety. A n argument can also be made for the use of current period weights, which necessitates the changing of weights with each successive period, while retaining the fixed base for purposes of price comparisons. If quantities purchased in the current period are used to weight both current and base period prices, the question price changes, but simply a ratio of budgets or total which the index answers is changed substantially. expenditures. The consumer’s standard of living may This type of index tells how much it currently costs relative price changes. In this illustration, neither of the implicit weights is the desired one. Some pro cedure for explicitly weighting the items according to their relative importance in the consumer’s total budget is needed in order to get a valid indication of the true impact of price changes upon the con sumer. Choice of Weights T h e kinds of w eights needed to correct the bias resulting from the simple index methods are obvious. A n indication of the relative importance of individual items in the consumer’s budget can be obtained from the quantities he pur chases. It is known, of course, that consumers change the mix of their purchases in response to changes in prices, depending upon whether individual items are necessities or luxuries. Business purchasers pre sumably do the same to the extent that substitution of items is possible. A difficult question to resolve, therefore, is what quantities to use as weights. For example, in Table I, the consumer’s total budget or expenditure in year 1 was $3,357.50 (i.e., S p ^ ) . His total expenditure in year 2 was $3,666.50 (i.e., 2 p 2q2)- A ratio of these expendi tures would not result in a valid price index under most circumstances. Since quantities change as well Table II SELECTED PRICE INDEXES FOR THE HYPOTHETICAL CON SUM ER (Prices and Q uantities from Table I) Sim ple Indexes Y e ar Simple A verage of Relatives Index M edian of Relatives Index Geom etric A verage of Relatives Index Harm onic A verage of Relatives Index Sim ple A g gregative Index 1 2 3 4 100.0 114.3 135.4 148.3 100.0 110.0 125.0 158.8 100.0 113.9 134.5 146.2 100.0 113.5 133.7 144.1 100.0 109.9 125.4 127.7 W eighted and W eighted C hain ed W eighted A g gregative Index Laspeyres Type W eighted A g gregative Index Paasche Type W eighted A verag e of Relatives Index Base V alue W eights 1 100.0 100.0 109.2 126.1 139.1 100.0 109.1 127.3 137.4 100.0 2 109.2 126.1 139.1 109.2 127.5 139.8 Year 3 4 W eighted A v e ra g e of Relatives Index Current V alue W eights Indexes Fisher's " Id e a l" Index Edgew orth's Index 100.0 109.1 126.7 138.2 109.1 126.5 138.3 100.0 W eighted A g gregative Laspeyres Type Index C hained 100.0 109.2 126.1 158.3 5 the consumer to obtain a given selection of items in relation to how much it would, have cost him to obtain the same selection in the base period. This is an important question, of course, but period to period comparisons are somewhat more difficult than with the fixed-weight, fixed-base type. In either case, the indexes compare an actual quantity with a hypothetical quantity. In the first case, the index compares a hypothetical expenditure (base period quantities at current prices) with an actual expenditure (base period quantities at base period prices) made in the base period. The first of these quantities may not be what the consumer really buys if he shifts his purchases due to the price changes. The second type of index compares an actual expenditure (current period quantities at cur rent period prices) with a hypothetical expenditure (current period quantities at base period prices). The latter of these quantities may not represent what the consumer actually would have bought if current period prices had prevailed in the base period. Weighted Aggregative Indexes— The Laspeyres Type T h e m ost com m on ly accepted w eighted price index of the fixed-weight and fixed-base type is that developed by Etienne Laspeyres in 1864. For the consumer represented in Table I, this index results in a value for year 2 of Ii ^ S p a q i/ S p iq ^ '109.2. The values of this index for the four years are shown in Table II. The index is of the weighted ag gregative type since it is the ratio of two expendi tures-—the numerator being the hypothetical current expenditure, and the denominator being the actual base period expenditure.4 A strict interpretation of the value, 109.2, given above for this consumer is that it would cost him 9.2 percent more to purchase the identical “ market basket” in year 2— if he desires to purchase it— than it cost him in the base year. Similarly, the same selections would cost him 39.1 percent more in the as weights, is the one developed by H. Paasche in 1874. For the consumer in Table I, for year 2, the index number is Ii 2= S p 2q2/S p 1q2= 109.1. Other values are shown in Table II. This index, like the Laspeyres, is a ratio of weighted aggregates. But it relates an actual current period expenditure in the numerator to a hypothetical base period ex penditure in the denominator.5 The interpretation of the Paasche number for this consumer is that it costs him 9.1 percent more to purchase the “ market basket" which he bought in the current period than it would have cost him in the base period. Again, this index reduces the upward bias present in the simple indexes for this consumer. In this illustration, a lack of sufficient variation in the quantities purchased between years 1 and 2 re sults in the Paasche and Laspeyres index numbers being very close together. For example, if this con sumer had reacted to the increase in automobile prices by not buying one in year 2, the Paasche index which is affected by current period quantities would have been 107.9. The Laspeyres index for year 2 would not have been affected by the con sumer’s decision not to purchase an automobile since only base period quantities are relevant. Thus, the Laspeyres number would have remained 109.2. An important difference in the kinds of interpreta tions which may be made of these indexes should be noted. Table II shows the Laspeyres index to be 109.2 in year 2 and 126.1 in year 3. It may be con cluded, therefore, that the cost of the “ market basket” increased 15.5 percent between years 2 and 3 (i.e., (126.1— 1 0 9 .2 )/1 0 9 .2 = .1 5 5 ). The “ market basket” which the consumer purchased in the base period would cost him 15.5 percent more in year 3 than it would have in year 2. A similar interpretation of the change in the Paasche index between these two years, however, would be incorrect. Each successive Paasche index number compares the current period fourth year than in the base year, as shown in “ market basket” Table II. This index construction reduces the bias selection actually purchased in year 3 cost the con directly to the base year. The introduced into the simple indexes by the large re sumer 27.3 percent more than it would have cost in lative increase in the price of movie tickets or by the base year, and the selection actually purchased the large absolute change in the price of auto in year 2 cost 9.1 percent more than it would have mobiles in year 2. cost in the base year. Weighted Type A Aggregative w eighted Indexes— The index of the Paasche second type described above, which uses current period quantities 4 Fisher, Irving. The M aking o f Index Num bers. Company, New York, 1922. p. 59. 6 Since the particular selection of commodities being priced changes between years 2 and 3, a direct comparison of the index numbers to measure price changes between the two years would be inappropriate. Houghton M ifflin 5 Ibid. A difficulty of this type in the interpretation of the G N P Deflator will be dis cussed in the final part of this article. Laspeyres and Paasche Compared Both of the weighted aggregative indexes appear to be superior to any of the previously discussed simple indexes. They reduce the likelihood of misleading movements in the indexes due to large relative changes in prices of items which may be of little importance in the consumer’s total budget, or due to large absolute changes which may be small in relation to the price of the item. They are free of the problems associated with the units for which the price is quoted. A g gregation of values or total expenditures is used in stead of aggregation of simple prices or price re latives. There is a considerable body of literature on the Laspeyres and Paasche indexes, and numerous arguments for and against the use of each of them have been advanced. W hile it is beyond the scope of this article to review all the literature, some of the arguments are particularly pertinent to this dis cussion, since, as will be shown later, the Laspeyres index is in essence the one used by the Bureau of Labor Statistics in constructing the Consumer Price Index. If a choice must be made between the Laspeyres and Paasche index numbers, it would seem that on logical grounds the Laspeyres index provides the answer to the question most commonly asked in index number applications, namely, the change in the cost of the base year “ market basket.” There are certain other arguments, however, affecting the choice be tween the two approaches— ignoring for the moment any sampling problems which may be involved. It has been argued that the Laspeyres formula has a tendency to overestimate price changes, while the Paasche formula tends to underestimate price changes. The argument is that the hypothetical ex penditure, Sp2qi, used in the numerator of the Laspeyres index would probably not be the actual expenditure that the consumer would make in year 2 if he were furnished with that amount of money. The sum, 2p 2qi, would be sufficient to allow the consumer to obtain the base period “ market basket,” but in a period of generally rising prices, that sum would be larger than the base period expenditures, ^PiTi- Thus, the rational consumer would tend to adjust his purchases, including the substitution of is somewhat overstated by the Laspeyres index. The Paasche index, on the other hand, contains the hypothetical expenditure S p ^ , in the denomi nator for year 2. In a period of generally rising prices this sum is lower than the numerator, Sp2q2, which represents the current period’s actual expendi ture. Thus, the argument is that if the lower sum of money had been given to the consumer in the base period, he probably would have adjusted to a dif ferent set of commodities that would have yielded him the highest possible standard of living for that total expenditure rather than necessarily the “ market basket” he would choose in year 2 when he has a higher sum available. T o the extent that this is true, the measure of price change applicable to the con sumer is likely to be understated by the Paasche formula. These arguments, advanced by Mudgett,6 do not necessarily mean that in all cases the two indexes are biased, nor do they imply that the Laspeyres number is necessarily greater than the Paasche, since actual quantities purchased respond to economic factors too numerous to evaluate. It is possible that particular economic circumstances may create biases in the opposite direction from those mentioned above. For example, if consumers shift purchases toward goods or services that are advancing rapidly in price, the use of base period quantity weights in the Laspeyres index may cause it to underestimate actual price changes. T o the extent that biases exist, they cannot be quantified because what the consumer might have done cannot be experimentally observed. These po tential weaknesses, however, illustrate why it is frequently argued that neither of the indexes pro vides a valid measure of changes in the cost of living. A cost of living index should measure the change in the cost of obtaining a given standard of living from one period to another. Living standards are de termined subjectively by the consumer, and he does in fact shift his purchases in response to changing prices in order to avoid giving up a customary standard or to obtain a higher one. Therefore, an index which cannot take into consideration such ad justments, and thereby hold constant a given standard of living to measure the change in the cost of ob taining it, cannot be a reliable index of the cost of living.7 some items for those in the original “ market basket” to allow him the same standard of living as before without having to duplicate the base period pur chases exactly. T o the extent that this is true, the measure of price change applicable to the consumer 6 Mudgett, Index N um bers, pp . 34-40. 7 The problems of constructing cost o f living indexes have resulted in extensive research. For detailed discussion, see Ulm er, M . J., The E conom ic Th eory o f Cost o f Livin g Index N um bers, Columbia U niversity Press, New York, 1949; Frisch, Ragnar, “ Some Basic Principles o f Price o f Living M easurem ents,” Econom etrica, Octo ber, 1954; and Konus, A . A ., “ The Problem o f the True Index of the Cost o f L ivin g ,” E conometrica, January, 1939. 7 Fisher’s “ Ideal” and Edgeworth’s Indexes C on cern about potential biases in the Laspeyres and Paasche indexes led Fisher to develop a number of tests for estimating the magnitude of error in various index number formulas.8 The result of these efforts was Fisher’s “ Ideal” index which recognized the op posing tendencies toward bias in the Laspeyres and Paasche approaches. The “ Ideal” index is the geometric average of the Laspeyres and Paasche in dexes. A geometric average is the n-th root of the product of n numbers (i.e., the geometric average of two index numbers is the square root of their product), and it always yields a value somewhat lower than a simple arithmetic average. Thus, the “ Ideal” index is closer to the lower of the Laspeyres or Paasche results. The values of this index are given for the hypothetical consumer in Table II. Due to computational difficulties involved in the practical application of the “ Ideal” index to large samples of price data, Edgeworth developed a close approximation which makes use of quantity data for both the base and current periods. Edgeworth’s index is defined as 11 2 = 2 ( q, + q , ) p 2/S ( qt■ + q 2) p ,, where year 1 is the base. For comparison, values of this index for the hypothetical consumer are also shown in Table II.9 Weighted Average of Relatives Indexes In terms of conceptual differences, the indexes already dis cussed essentially cover the field. The weighted average of relatives index number differs not so much in concept as in formula construction— a fact which has important practical value in the calculation of the index. It was noted in the discussion of weighted aggregative indexes that prices are weighted by quantities purchased. By comparison, the weighted average of relatives index weights price relatives (ratios of prices) by total expenditures (values of purchases). A choice must be made again between base period or current period expenditures as the weights. Consider first this type of index using base period expenditures as weights (i.e.. base value weights). The index for year 2, where year 1 is the diture in the base period, p ^ , for an individual com modity. The weight is multiplied by the price ratio and these quantities are summed for all items in the “ market basket.’ The denominator is the base period expenditure on all items in the “ market basket.” It can be seen above that p /s in the numerator cancel so that the formula reduces algebraically and is identical to the Laspeyres type weighted aggregative index. This is not the important distinction, how ever, because the formula is used as it is shown rather than in its reduced form. As a practical mat ter, quantities purchased are seldom readily available which makes the direct application of the Laspeyres formula difficult. But prices of items and actual expenditures on individual items are more readily available, which means that the weighted average of relatives index can be applied more easily than any of the other weighted indexes discussed. W ith minor modification, this index is the one applied by the Bureau of Labor Statistics in deriving the Consumer Price Index, and, therefore, the result is the same as the Laspeyres method.10 It is also possible to construct a weighted average of relatives index with current value weights by substituting current period expenditures, p2q2, in the numerator and the total of current period expendi tures for the given “ market basket,” 2 p 2q2, in the denominator. This index does not reduce to the Paasche weighted aggregative index, but it is easier to apply than the Paasche index for the same reasons as those given above. This construction is known as the Palgrave index formula. It has received little at tention by students of index numbers since Fisher,11 and is discussed here only for completeness. For comparison, the values of the two weighted average of relatives indexes are given in Table II for the hypothetical consumer. Chain Indexes A ll of the indexes discussed thus far have been fixed-base indexes. That is, it is as sumed that the base period upon which the index is computed does not change with each successive period. Chain indexes involve a constantly shifting base period. The use of a fixed-base index assumes that the span of time between the base period and the current base is period is sufficiently homogeneous to allow a valid p2 Ii 2= : p7 * '- l V h The price relative is the simple ratio of prices p2/p i- The base value weight is the total expen ; Fisher, The M aking o f Index N um bers, Ch. 11. 1Mills, Statistical Methods, Ch. 13. s comparison of prices in the current year with those in the base year. It is obvious that this is a dif ficult assumption to satisfy fully when economic circumstances are rapidly changing and technological Ibid. 11 Fisher, The Making o f Index N um bers, Ch. 3. progress is occurring which affects the quality of items covered by the index. A t best it means that frequent updating of the weights and revision of the sample of commodities in the “ market basket” are essential. A fixed-base index with base period weights is particularly suspect in this connection, and this is the concept used in constructing most major price indexes in use today. A fixed-base index using current period weights such as the Paasche type is perhaps less subject to criticism on this score although it is questionable whether such an index gives the most useful measure in the first place. Even so, base period prices are still the basis of comparison. Given that an index of the Laspeyres type is the preferred concept, the problem of how to make it consistently valid over any reasonably long period of time becomes significant. A fixed-base index with base period weights for any given year is independent of price changes that have occurred in any year between the current one and the base year. Intervening price changes, how ever, may have significantly affected spending pat terns. A chain index is an expedient measure for resolving this difficulty. The procedure entails up dating the base one period at a time so that the index for any given period uses the previous period as a base. The indexes are then linked together in a multiplicative fashion. Using the Laspeyres for mula as an example, than in any other two successive years in this il lustration. The effect of the chaining procedure is evident in the value of I x 4, which shows the com pounded result of the price rises of each successive year. It is also possible that any consistent biases present in the index formula will lead to cumulative error by chaining. The chained Laspeyres index in dicates price increases to be 13.8 percent greater between years 1 and 4 than the fixed-base Laspeyres index (i.e., 158.3 vs. 139.1). W hile the divergence between the two indexes is large in the fourth year, the example does not imply that the chain method is invalid as such. The use of the chain method has been urged by Mudgett as one means of keeping the index close to the market situation.12 It allows for the shifting of purchases in response to changes in prices more readily than does the fixed-base type. Thus, in a period of rapidly changing prices, such as the cur rent period, the chain method has some attraction, particularly as a supplement to a fixed-base index. The difficulties involved in the interpretation of chain indexes, however, as well as their tendency to magnify successions of sharp price changes pose serious problems. The chain index alone, therefore, is not generally regarded as a satisfactory solution to the problem associated with fixed-base indexes— namely, the need for periodic revisions of the “ market basket.” Statistical Problems I j 2 -----^ P 2 * I l / ^ P l (I l> I 2 3— 2p3q2/ 2 p 2q2, and I x 3— I x 2 I 2 3, etc. The chain index for year 3 uses the quantities pur chased in year 2 as weights. The index for any given year can be expressed with any earlier year as the base by multiplying the indexes starting with that earlier year. Table II shows values of the chained Laspeyres index, for the hypothetical consumer, using year 1 as the base. Table III gives all combinations of the chained Laspeyres index for the four years. Table III CHAINED LASPEYRES INDEX FOR HYPOTHETICAL CONSUM ER (Prices and Q uantities from Table I) I, „= 1 09 .2 1, 3=126.1 I 2 3=115.5 1, 4= 1 58 .3 I 2 4=145.1 I 3 4= 1 25 .5 There are still a number of statistical problems which remain even after an appropriate index num ber concept has been selected. This is particularly true of a general-purpose index in which the coverage of items is broad and where the index is used to represent the behavior of prices in general. These are features of the published indexes of wholesale and consumer prices. W hile there are stated limita tions as to the interpretations that may be made from these indexes, their usage has evolved in such a way that they are regarded as broad indicators of price changes. The remainder of this part of this article serves only to list and explain the nature of the statistical problems involved in the construction of price index numbers. This discussion is not a review of pro cedures in actual use by those government agencies or others who produce the indexes in current use. but is a more general explanation of the types of problems to be encountered by anyone involved in the construction of price indexes. These problems are Price increases occurring between years 3 and 4. as measured by the Laspeyres formula, are larger 12 Mudgett, Index N um bers, pp. 70-78. 9 related in more detail to the procedures employed in developing the commonly used indexes of wholesale and consumer prices in the final part. Sam pling of Item s It is certainly not feasible to derive a price index for consumers which takes into consideration all goods and services that con sumers buy. N or is it possible to obtain a wholesale index of prices covering all manufactured industrial items, all raw materials, and all farm products. Therefore, an index intended for broad usage must rely on representative samples of items. The design of the sample is thus critically important in determin ing the quality of the index. Just as there are im portant differences in spending patterns among urban and rural families, central-city and suburban families, and northern and southern families, there are im portant differences among individual families within each of these groups. For these reasons there is no single index applicable to all consumers. The Con sumer Price Index, for example, which is limited in coverage to those goods and services representative of the budgets of urban wage earners and clerical workers, still covers a diverse group. The selection of the sample of goods and services to be included in the “ market basket,” therefore, must depend upon a valid survey of spending patterns within the group to which the index is to be applicable. Sam pling O ver T im e O nce the coverage of the index as to groups of consumers or industries is de fined and the selection of items in the “ market basket” is specified, the question remains of how frequently to observe the prices of the items included. It must be decided whether the index is to be pub lished monthly, quarterly, annually, or by some other period. Under theoretically ideal circumstances, a continuous observation of prices would be desired. For obvious reasons, the cost of such a procedure Sam pling O ver G eographic A reas The commonly used aggregate indexes of prices are published on a national basis. Whether the index is of a specialpurpose or general-purpose nature, it is known that its applicability is not the same in all parts of the nation in most cases. Just as general economic con ditions vary widely among sub-national regions, price changes may vary widely by area. This is par ticularly true of indexes of consumer prices which include numerous services and highly processed goods. Items which are essentially the same every where, for which highly organized national markets exist, and for which there is little variation in costs of production and delivery are less subject to this problem (e.g., some of the items included in the index of basic commodity prices). If it is desired that a price index (e.g., of con sumer items) be generally applicable to a wide geo graphic area, an appropriate means of sampling among different places must be derived as well as a weighting scheme for assembling the information into a single index. Even so, some error is inevitable in the application of an index derived on this basis to any particular area. The effect of such error is practically impossible to estimate without construct ing separate indexes periodically for the specific area in question. Some indexes, such as the Consumer Price Index, are published on a national basis and by narrower regions such as Standard Metropolitan Statistical Areas. W hile it is clearly not practical to construct price indexes for every city in the nation, it is possible to vary sample cities on a probability sampling basis and thus provide a means of determin ing the error involved in the estimate of the national figure. Such a procedure possibly has merit in the sense of providing better national indexes, but it does not eliminate the error involved in applying a national index to a particular location. every three months, previous experience with the Q uality Changes and Changes In Tastes O ne oi the most difficult problems to resolve in price index construction is the need to adjust the “ market basket’ to reflect technological change which affects the quality of goods and services purchased, and to re flect changes in tastes and preferences of buyers These problems, like the geographic area problem are more serious in an index which measures con sumer prices than in one which measures prices oi “ market basket” may provide sufficient information items at a lower stage of processing or basic com would exceed the practical benefit. A satisfactory compromise on the problem can be reached if periodic samples of prices are used, and if acceptable means of estimating interim prices can be derived for those periods between benchmark samples. For in stance, if it is desired that a price index be pub lished monthly, and samples of prices are obtained to allow estimation of prices and therefore of the modities. index for the intervening months. Short-term move costs, and numerous other industrial items, however Machinery and equipment, constructor ments in an index obtained on this basis are, of also undergo technological and quality change whicl course, subject to error, particularly as underlying poses similar problems for indexes of industrial 01 economic circumstances change. wholesale prices. 10 It is obvious that a television set purchased in 1970 is quite a different item from one purchased in 1957. It is a higher quality, more sophisticated piece of equipment. The same is true of many consumer goods and services such as automobiles, airplane trips, and refrigerators, as well as machine tools and trucks used by industry. The prices of many of these items have risen in recent years. Part of the price increase, however, is due to the quality improvement and should somehow be eliminated in measuring the price change associated with the original “ market basket.” Without actually renewing the “ market basket,” the only generally satisfactory solution to this problem requires gradually splicing in the new or improved item, while at the same time, gradually removing the old item. This prevents disruption of the continuity of the index which would result from an abrupt substitution of the item in the “ market basket.” A s a practical matter, however, the rapidity of technological progress has made this a major problem in constructing indexes of consumer and industrial prices. Changes in consumer tastes present the same kind of problem. As such things as garters, bed warmers, and washtubs have declined in the preference scales of consumers, the “ market basket” has required up dating to include entirely new products such as panty hose, electric blankets, and automatic washers. The same problem occurs among industrial items as in the case of textile goods where the gradual sub stitution of synthetic fibers for cotton has taken place due to changes in the preferences of garment producers. This problem coupled with that of quality changes necessitates continuous review of the current validity of the “ market basket.” Transaction Prices vs. List Prices It is a basic requirement of all price indexes that prices used in calculating the index be the actual prices at which transactions are made. Often, however, quoted prices do not change while significant changes occur in prices actually paid. Experience has shown this to be a problem particularly in the measurement of industrial prices. Most prices used in the Wholesale Price Index, for example, are sellers’ list prices. Stigler and Kindahl recently contended that these prices bear little resemblance to the prices actually paid on many industrial items with the result that the Wholesale Price Index overstates industrial prices by failing to take cognizance of discounts, special offers, and price shading. Their contention implies that the Wholesale Price Index understates the effect of changing economic conditions upon in dustrial prices.13 This is a significant point since the Wholesale Price Index is so closely watched as a barometer of inflation. The Consumer Price Index has not been subject to the same criticism since price observers function like buyers and obtain prices which they know in most instances represent the prices at which the goods and services can be purchased. Sampling Error In Indexes E ven if all statistical problems are satisfactorily dealt with in the con struction of price indexes, some error in the estimate of price levels and changes results. This is a phe nomenon of sampling which occurs even under the best of circumstances. A n important feature of sampling error, however, is that its magnitude can be estimated, and it generally decreases as the sample size increases. This feature makes it possible to state with some degree of confidence (i.e., at some level of probability) how far the calculated value of the index can be expected to vary on either side of its correct value. Estimates of sampling error are frequently published along with the major indexes. It can be a mistake, however, to interpret estimates of sampling error too literally because sampling de sign considerations and data problems render all major indexes in current use less than perfect on other grounds. SUMMARY The issues raised in this part are followed up and related in specific detail to the Bureau of Labor Statistics’ Consumer Price Index and Wholesale Price Index and to the Department of Commerce’s G N P Deflator in the final part which will appear in next month’s issue of this Review. William H. Wallace 13 Stigrler, George J. and Kindahl, James K . The Behavior o f In dustrial Prices. N ational Bureau o f Economic Research, N ew York, 1970. 11 PARITY, SUPPORT PRICES, DIRECT PAYMENTS, AND ALL THAT Recently, price and income support payments to agricultural producers have been closely scrutinized by politicians, economists, and the general public. A s a result Congress has enacted legislation that will limit the amount of money the Government can pay to any one producer. This article briefly reviews Government policy with respect to agriculture and some of the factors leading to payment limitation. Government involvement in agriculture has a long history. The Homestead A ct of 1862, the Morrill Act, the Hatch Act, and the Smith-Lever A ct were all landmarks in agricultural legislation. More di rect Government involvement with agriculture began in the 1930’s when price and income support pro grams were introduced to raise farm product prices and incomes of farm families. T erm in olog y T o understand the agricultural pro grams which are the subject of the current debate, it helps to know some of the terminology. Parity Price The concept of parity was introduced in the 1930’s to establish a standard or measuring rod against which farm prices might be compared to determine whether or not they were “ fair.” Farm prices are said to be at parity if they bear the same relationship to the prices of articles farmers buy as they did in the base period. The years 1910 to 1914 were selected as the base period since they repre sented a period in which the relationship between prices received and prices paid by farmers was very favorable to farmers. Over the years the formula for calculating parity prices has changed. The present method of calculat ing parity uses an adjusted base period. The ad justed base period for a commodity is obtained by dividing the average market price received by farmers for the commodity during the most recent ten-year period by the average index of all prices received by farmers for the same period. T o obtain the 1970 adjusted base price of corn, for example, the average price received by farmers for corn, adjusted to allow for unredeemed loans and other supplemental pay ments resulting from price support operations, in the period 1960-69 ($1.17 per bushel) is divided by the average index of price received by farmers, adjusted to include an allowance for unredeemed loans, etc., for the same ten-year period (257 on a 1910-14 base). The current parity price is obtained by 12 multiplying the adjusted base price by the current index of prices paid by farmers, including interest, taxes and wage rates. In August 1970, the index of prices paid (on a 1910-14 base) was 389. Thus, the August 1970 parity price for corn was $1.77 per bushel ($0.45 x 3 8 9 /1 0 0 ). The parity concept simply expresses arithmetically one idea of what is equitable or fair. Equity is a subjective concept; however, and there is no ob jective way to measure it. Shifting the base to a period other than 1910-14, for example, may have a substantial impact on current parity prices. Never theless, parity often figures prominently in farm policy discussion. Support Prices The nature of supply and demand for farm products causes their prices to be no toriously unstable. Because farm prices were un stable and because of the general economic depres sion at that time, price support programs for farm products were initiated in 1933, with the goal of raising farm prices to a parity level. Parity level support prices were sought through loan, purchase, and storage operations as well as through production control programs that authorized the Secretary of Agriculture to support different commodities at dif ferent percentages of parity. Originally, production control was voluntary but this failed and production control was made mandatory. Control of agricultural production, started at a time when many people were unemployed and without enough food to feed their families, brought forth a great deal of derision in its early years. One critic wrote the following letter to a newspaper: “ Mr. B. has a friend who received a Govern ment check this year for not raising hogs. So B now proposes to get a farm and go into the busi ness of not raising h o g s; says in fact not raising hogs appeals to him very strongly. O f course he will need a hired man and that is where I come in. I write you as to your opinion of the best kind of farm not to raise hogs on, the best strain of hogs not to raise, and how best to keep an inventory of hogs you are not raising. His friend who got the $1,000 got it for not raising 500 h o g s ; now we figure we might easily not raise 1,500 or even 2,000 hogs, so you see the possible profits are only limited by the number of hogs we do not raise.” 1 were replaced with direct cash payments to producers participating in the programs. Direct payments are used (1 ) to supplement income and (2 ) to con trol production by paying producers to restrict the acreage of certain crops. The new programs were supposed to raise prices by reducing crop production and by removing sur pluses from the market. They were not successful in raising prices during the 1930's, but where pro duction control and support programs had failed the war succeeded and farm prices rose to new highs. For some time after the war, the Farm Bloc in Congress succeeded in maintaining high wartime sup port prices. Meanwhile, world farm prices came under heavy downward pressure as Europe re covered. The results were predictable. By the end of the 1950’s high support prices and ineffective pro duction control were creating large surpluses despite substantial diversion of acreage from 1956 to 1959 under the acreage reserve and conservation reserve programs authorized by the Soil Bank Act. By the early 1960’s practically every grain and butter storage facility in the United States was filled. In 1961, the annual cost of owning and storing the $9 billion farm surplus was $1 billion. Increasing Costs Since their introduction in the early 1960’s, direct payments (primarily for the major field crops— cotton, wheat, and feed grains) have increased from $702 million to approximately $3.7 billion. Direct payments as a percent of realized net farm income in the United States increased from 6 % in 1960 to 23% in 1968 (Table I ) . The same pattern was evident in the Fifth District. Producers in W est Virginia and South Carolina received re spectively 20.7% and 35.7% of their realized net farm income from direct Government payments. in line with world prices and reduce Treasury costs. D istribution of B enefits M ost of the direct benefits from the price support and direct payments programs go to a relatively few producers operating large farms. Program benefits are concentrated on these larger farms which earn comparatively good incomes (Table I I ) . Measured by size of payment, the top one-fifth of the cotton, wheat, and feed grain producers received respectively 69% , 62% , and 56% of the program benefits, whereas the one-fifth with the smallest payments received 2 % , 3 % , and 1%. The 5% of the producers receiving the largest pay ments accounted for 4 1% , 39% , and 24% re spectively of the total benefits. Farm income re ceived by the top 20% of the recipients was more T o maintain farm income, high level support prices than one-half of the total farm income of all pro Direct Payments High support prices combined with attempts of the United States Government to sell farm products at above world prices stimulated production abroad. This policy led to a loss in the United States’ share of the world market, particularly in cotton, one of our major farm exports. Conse quently, support prices were reduced to bring them ducers receiving benefits. 1 Clair W ilcox, Public Policies Toward Business (Homewood, Illinois: Richard D. Irvin, Inc., 1 9 6 0 ), p. 462. Additional evidence which shows that payments TABLE I G overnm ent Payments as a Percentage of Realized Net Farm Income United States and Fifth District States, 1960-1968 V irginia W est V irginia Year M aryland 1960 3.6 3.8 6.4 1961 6.8 6.2 1962 6.9 7.8 1963 6.7 1964 7.2 1965 6.1 1966 5.5 1967 5.9 1968 6.4 Source: United States Departm ent of Agriculture. North C aro lin a South C aro lin a United States 2.2 9.5 6.0 8.7 5.2 10.4 11.8 9.4 6.2 11.4 13.8 7.9 11.3 5.2 10.5 13.5 7.5 12.3 5.6 12.2 16.7 8.3 11.6 8.2 15.5 17.6 9.5 13.2 9.9 27.7 20.1 10.1 24.2 10.0 30.2 21.6 10.4 20.7 11.1 35.7 23.0 13 TABLE II Distribution of Farm and Benefits of Selected Program s—Proportion of Income or Benefits Received by Selected Groups of Recipients United States, Selected Y e ars Percent of Benefits Received by Lower 20% of Recipients Item U pper 20% of Recipients Upper 5% of Recipie Sugarcane 1965 1.0 83.1 63.2 Cotton 1964 1.8 69.2 41.2 Rice 1963 1.0 65.3 34.6 W heat 1964 3.3 62.4 38.5 Feed grains 1964 1.0 56.1 23.9 Peanuts 1964 3.8 57.2 28.5 Tobacco 1965 3.9 52.3 24.9 Farm er and farm m anager total income 1963 3.2 50.5 20.8 Source: Jam es T. Bonnen,, "The Absence of Knowledg e of I An O bstacle to Effective Public Progr tributional Impacts A n a lysis and Decisions," Economic A n a lysis of Public Expenditure Decisions, The PPB System , (Joint Economic Com m ittee, U. S. C o n gress, M ay 1969) p. 440. go to a relatively few large scale producers is avail able. For example, 12,921 producers received pay ments of $20,000 or more in 1969. This figure was approximately one-half of 1% of all producers re ceiving payments, but these producers received 13.7% of the total payments (Table I I I ). The concentration of program benefits to the pro ducers of a relatively few commodities and to a fewlarge-scale producers has led many people to question the equity of the agricultural programs of the 1960’s. Proposals to Lim it Paym ents R ecently, efforts have been made to limit the size of direct cash pay ments to producers. The House of Representatives passed legislation in 1968 and 1969 to limit pay ments to $20,000 per producer but the Senate did not support payment limitation. In 1970, the Senate voted to limit payments to $20,000 per producer and the House passed a $55,000 per program limitation to producers of wheat, feed grains, and cotton. After reconsideration the Senate also approved a payment limitation of $55,000 per program. Supporters of payment limitation question the equity of current agricultural programs. They argue that it is hard to justify large payments to a few producers especially when public funds are needed for other problems such as education, job training, 1970 session, the most discussed level of limitation was $20,000 per individual and the idea of a $20,000 limit will likely be reintroduced when the 1970 farm legislation expires. Thus the remainder of this paper compares the impact of these two payment limits. P roducers of cotton, feed grains, and wheat will be most affected by payment limitations. In 1969, the number of cotton, feed grain, and wheat pro ducers receiving payments of $20,000 or more totaled 8,799 (Table I V ) . This number relates only to those producers who would be affected by a payment limitation on a single commodity. A total of 11,733 producers would have been affected in 1969 if the limitation applied to a combination of the three major commodity programs. In 1969, only 1,100 cotton, feed grain, and wheat producers received payments of $55,000 or more. Thus, a $55,000 per program limitation w ill affect on ly 1,100 producers. A $55,000 per program limitation on wheat, feed grains, and cotton amounts to a $165,000 limitation per pro ducer. V ery few farms, however, are large enough to collect $55,000 from more than one program. United States Department of Agriculture figures show that in 1969 only two producers received in excess of $50,000 from each of the three programs and 37 received $50,000 payments from two of these programs. John Schnittker, former Under Secretary of A gri culture, estimated that a $20,000 limitation per pro ducer would have saved the Treasury $206 million in 1967.2 Using 1969 data, the United States D e partment of Agriculture estimated that a $55,000 per program limitation would have saved $58.3 million. Payment limitations will clearly have the greatest impact on cotton producers (Table I V ) . 2 John A . Schnittker, “ The Distribution o f Benefits From E xisting and Prospective Farm Program s,” reproduced in The Congressional Record, Vol. 115, June 1969, N o. 98, p. H 4836. TABLE III Frequency Distribution of Producer Payments Under A gricultural Stabilization and Conservation Service Programs United States, 1969 Paym ent Range Less than $20,000 Num ber Percent Million Dollars Percent 86.29 2,504,383 99.48 3,188.5 $20,000 - $49,999 10,970 .44 315.0 8.52 More than $50,000 1,951 .08 191.7 5.19 2,517,304 100.00 3,695.2 100.00 health, pollution control, and food aid programs. Total Im pact of Paym ent Lim itations U ntil C ongress voted for a $55,000 per program limitation in the Source: The C on gressional No. 114, p. S I 0806. 14 In 1969, the 6,194 cotton payees who received payments of Record, Volum e 116, Ju ly 8, 1970, $20,000 or more were paid $262.6 million and the 949 payees receiving payments of $55,000 or more were paid $103.8 million. Im pact on the Fifth D istrict In the Fifth D is trict very few producers will be affected by either a $20,000 per producer or a $55,000 per program limitation (Table V ) . A few producers in North and South Carolina will be directly affected. In 1969 a payment limitation of $55,000 per program would have affected three cotton and three feed grain pro ducers in North Carolina, and 13 cotton producers in South Carolina. Total payment reductions to these two states would have been $600,000 and $400,000 respectively. E ffect of Paym ent Lim itations on Production D irect paym ents are made to supplem ent farm incom e and to encourage producers to restrict acreages of certain crops. The Department of A gri culture estimates that approximately 65% of all di rect payments are for resource adjustment purposes. In other words this is the price that farmers are paid TABLE IV Producers Receiving A gricultural Stabilization and Conservation Service Program Payments G reater Than The Indicated Amount United States, 1969 Program Cotton Feed G ra in W heat Cotton, Feed G ra in and W h e at1 Total Recipients Paym ents of $20,000 or more Payments < $55,000 or more 445,155 6,194 949 1,641,863 1,482 98 995,371 1,123 53 2,125,491 11,733 1,100 TABLE V Producers Receiving Paym ents of More Than The Indicated Amount Fifth District, 1969 Producers Receiving Paym ents of S ta te C o tto n Feed G ra in M aryland 3 V irginia 2 W heat Cotton Feed G ra in W heat W est V irginia North C aro lin a 38 14 .... 3 South C aro lin a 201 6 .... 13 Source: The C ongressional Record, Volum e 116, July 8, 1970, No. 114, p. S10806 and House of Representatives, Report No. 91-1329, 91st Congress, 2d session, July 23, 1970, p. 17. to divert part of their cropland acreage from pro duction. The amount diverted varies from year to year. Opponents of payment limitation argue that a limitation may cause large-scale producers not to participate in production control programs and thus destroy the effectiveness of such programs. H ow ever, both Schnittker3 and Mangum4 present per suasive arguments that payment limitations as low as $20,000 per producer will not seriously affect program participation. Sum m ary C ongress recently voted to limit direct payments to producers of wheat, feed grains, and cotton. This action was the result of public con cern about the cost of the programs and the distribu tion of benefits. The impact of the limitation will be mostly on cotton producers. Am ong producers in the Fifth District, it would appear that only 19 pro ducers in North Carolina and South Carolina will be affected. Thomas E. Snider 1 Does not equal total for cotton, feed grain and w heat because some producers receive paym ents from more than one program . Source: The Congressional Record, Volum e 116, July 8, 1970, No. 114, p. S10806 and House of Representatives Report No. 91-13129, 91st Congress, 2d session, July 23, 1970, p. 17. 3 John A . Schnittker, op. cit., p. H 4836. 1 Fred A . M angum , “ The Case for Paym ent Lim itations,” talk presented at Southern Region Extension Public A ffa irs Committee Meeting, New Orleans, March 25, 1969. 15
@FedFRASER