Noes on Price Indexes and Inflaion Professor John Yinger The Maxwell School Syracuse Universiy Inroducion The prices of goods and services are no consan over ime. A general increase in prices, also known as inflaion, leads o a decrease in he volume of goods and services ha can be purchased wih a given amoun of money. Price indexes, such as he wellknown consumer price index, or CPI, are a ool for measuring he relaive purchasing power of money, ha is, he volume of goods and services ha can be purchased in one ime period relaive o anoher. Calculaing a Price Index To calculae a price index, one mus begin wih a marke baske of goods and services consumed by a ypical household. This marke baske consiss of quaniies purchased by a ypical household during a year. Thus, he marke baske consiss of pounds of chicken, boles of beer, pairs of pans, and so on. The marke baske could reflec acual consumpion in a paricular year or could be some muli-year average. The issues o be considered in selecing he marke baske are discussed in he las secion of hese noes. In any given year, each iem in he marke baske sells for a paricular price per uni. Now le Q be he quaniy of good (or service) i in he marke baske in and le i Pi be he price of good i in year. Then if here are N goods and services in he marke baske, we can wrie he spending required o purchase he marke baske in year, S, as follows: S = P Q P Q... P Q 1 1 2 2 N N A price index is simply he spending required o purchase he marke baske in year relaive o some base year. The role of he base year mus be recognized. A price index does no indicae he purchasing power of money in any absolue sense bu only relaive o some base year. For example, a price index can indicae how much purchasing power has changed since las year or over he las decade. Thus, he selecion of he base year depends on he quesion one is asking and, as we will see, one can easily swich from one base year o anoher.
2 Now suppose he base year is 2000 (a base year used in some federal saisics). Then he price index in year, I, is defined o be I S = 100 S 2000 Noe ha he 100 in his definiion is purely for convenience. I is easier o alk abou a price index of 106 han a price index of 1.06. Because a price index canno be calculaed wihou selecing a base year, le us rewrie his equaion wih he base year idenified: I S 2000 = 100 S 2000 Thus, a price index indicaes he cos of a marke baske of goods in a given year relaive o some base year. If a price index has a value of 105, i indicaes ha he prices have risen 5 percen since he base year. A price index of 200 indicaes ha he prices have doubled, and a price index of 50 indicaes ha prices have been cu in half. Real Versus Nominal Dollars The principal use of price indexes is o ranslae daa from nominal o real erms or visa versa. Daa in nominal erms are expressed in acual or curren dollars, which are defined o be dollars as hey acually appear. If your acual income is $50,000 for example, hen your income in curren dollars (or, equivalenly, in nominal erms) also is $50,000. Daa in real erms are expressed in consan dollars, which are defined o be dollars of equal purchasing power o ha in some base year. Thus consan dollars, like price indexes hemselves, canno be defined wihou a base year. The disincion beween curren and consan dollars (or, equivalenly, beween nominal and real dollars) is imporan because we ofen wan o deermine wha has happened o someone s abiliy o purchase goods and services. If we wan o know wheher people are as well off oday as hey were in 1980, for example, i makes no sense o compare heir acual incomes in hose wo years because $1 of income received in 1980 could purchase more goods and services han $1 of income received oday. To compare consumers purchasing power in wo differen years, herefore, we mus express heir incomes in real erms (or, equivalenly, in consan dollars). Tha s where price indexes come in. The links beween real (consan) and nominal (curren) dollars are given by he following equaions:
3 Nominal Real = Price Index/100 or, equivalenly, Curren Consan = Price Index/100 Don be confused by he 100 in hese equaions. Remember ha price index is muliplied by 100 jus o make i look prey. These equaions need precision, no looks, so we have o remove he 100. Now suppose you observe ha he income in a paricular occupaion is $50,000 oday and ha prices have doubled since 1980. A doubling of prices means ha $1 oday can purchase only half as much as i could in 1980. I also means ha he oday s price index (wih 1980 as a base) is 200. In his case, he income in his occupaion in consan 1980 dollars is only $50,000/(200/100) = $50,000/2 = $25,000. Here is a slighly more complicaed example. Suppose one wans o compare an acual income of $25,000 in 1980 wih a $50,000 income in 2000. Suppose furher ha one has obained a published price index, wih a 1983 base, equal o 82.4 in 1980 and 172.2 in 2000. Then real income wih a 1983 base is $25,000/(82.4/100) = $30,340 in 1980 and $50,000/(172.2/100) = $29,036 in 1990. Even hough nominal income is wice as high in 2000, in oher words, real income is slighly higher in 1980. A word of cauion: In focusing on price indexes, people ofen forge ha prices are no he only economic variable ha changes over ime. Even if prices double over some ime period, people will no be any worse off if heir incomes also double. In fac, he general phenomenon of inflaion ends o affec incomes as well as prices so ha inflaionary periods are no necessarily, or even usually, periods of falling real incomes. This is no o say ha inflaion is neural. Many analyss argue ha inflaion, paricularly unanicipaed inflaion, disrups invesmen plans and undercus economic growh. Bu i is o say ha inflaion, paricularly seady, anicipaed inflaion, is no necessarily harmful o an economy. Insead of assuming ha price increases make people worse off, one should use price indexes o deermine wheher process have increased faser han incomes, ha is, wheher real incomes have fallen. Anoher common misconcepion is ha inflaion hurs he poor. In fac, many poor people are insulaed agains inflaion by eiher ransfer paymens ha increase auomaically or wages ha end o increase wih inflaion. The major losers during an inflaionary period are rich people who hold ineres-bearing asses, which lose value when unanicipaed inflaion occurs. In mos cases, inflaion does no harm he lowes
4 income classes bu significanly reduces he average real incomes of he highes income classes. 1 Someimes one may wan o change a price index from one base o anoher. To compare wo differen price indexes, for example, one mus express hem boh in erms of he same base year. Translaion from one base year o anoher is sraighforward. Consider he change from base year b o base year c. From he definiion of a price index, we find ha and S I c = 100 S S I b = 100 S c b So I c S S S S 100 100 = I b S S S S I b Ib b b c b c c c /100 In words, one can change an index wih base year b ino an index for base year c simply by dividing he original index by is own value in year c (wih he 100 removed). Suppose, for example, ha you wan o change a price index from a 1983 base o a 2000 base. Then if, as in an earlier example, he price index for 2000 using he 1983 base is 172.2, one can ranslae he price index wih a 1983 base ino a price index wih a 2000 base simply by dividing he former by 1.722. Thus, if he price index for 2004 using a 1983 base is 188.9, hen he price index for 2004 using a 2000 base is 188.9/1.722 = 109.7. Noe ha changing he base year does no change one s conclusions abou he exen o which prices have increased or decreased. In he above example, he price index wih a 1983 base wen from 172.2 in 2000 o 188.9 in 2004. Thus prices increased by (188.9-172.2)/172.2 = 9.7 percen over his period. The price index wih a 2000 base wen from 100 in 2000 o 109.7 in 2004, which also corresponds o a 9.7 percen increase. 1 See, for example, Joseph J. Minarki, The Size Disribuion of Income During Inflaion, The Review of Income and Wealh, December 1979.
5 Selecing a Price Index Many differen price indexes are published: he CPI, he wholesale price index, and a whole series of implici price deflaors ha are used in naional income accouning. These implici price deflaors include one for personal consumpion expendiures and one for sae and local governmen purchases. Differen price indexes are appropriae in differen conexs. To measure price changes facing consumers, one should use he CPI or he implici price deflaor for personal consumpion expendiures. Alhough he CPI is well known, i has some echnical problems, especially in is reamen of housing. As a resul, many analyss believe ha he CPI exaggeraes inflaion and prefer he personal consumpion deflaor. 2 To measure price changes facing sae and local governmens, one obviously should use he implici price deflaor for sae and local governmen purchases. For purposes of comparison, Table 1 liss hree differen price indexes over he 1960-2004 period. Disposable (ha is, afer-ax) personal income per capia also is presened. The firs price index, he CPI, has a base year se a he average of 1982 o 1984. The oher wo indexes have a base year of 2000. According o he CPI, prices are more han six imes as high oday as hey were in 1960 (188.8/29.6 = 6.38). The personal consumpion deflaor shows a smaller increase in prices (107.8/20.8 = 5.28), whereas he implici deflaor for sae and local governmen purchases shows a larger increase (112.2/14/7 = 7.63). Using he CPI, we can also deermine ha real income (in 1982-84 dollars) has increased from ($2,022/0.296) = $6,831 in 1960 o ($29.334/1.078) = $15,529 in 2004. This is an increase of ($15,529 - $6,831)/$6.831 = 1.27 = 127 percen. As an exercise, resae he CPI wih a 2000 base and compare i wih he implici deflaor for personal consumpion expendiures. Which index indicaes a greaer price increase beween 2000 and 2004? As anoher exercise, use he personal consumpion deflaor o ranslae disposable income ino consan dollars. How much did real disposable income increase beween 1960 and 2004 using his price index? The Index Number Problem Finally, a echnical problem, called he index number problem, arises wih all price indexes (as well as wih many oher kinds of indexes). The problem is ha he composiion of he marke baske, ha is, he se of purchases by a ypical household, changes over ime. This change has several causes. Increases in income lead people o shif ou some goods ino ohers. The number of children in he ypical family (or some oher demographic characerisic) may change and hereby aler he consumpion of 2 For a discussion of he problems wih he CPI, see Charles L. Schulze, The Consumer Price Index: Concepual Issues and Pracical Suggesions, Journal of Economic Perspecives, Winer 2003, pp. 3-22. Available hrough www.jsor.org.
6 goods designed for children. Relaive prices may change, and people will subsiue away from goods wih relaive price increases o goods for which relaive prices decrease. Because he marke baske changes over ime, he definiion of he marke baske iself, namely he Qi s defined earlier, becomes ambiguous. Should one use he consumpion paern in he base year, in he curren year, or in some inermediae year? The answer o his quesion maers because i can aler he sory old by a price index. Suppose ha beween wo years people sop purchasing a good he price of which increases more rapidly han he prices of all oher goods. Then using he consumpion paern in he firs year will yield a price index ha increases more rapidly han an index using he consumpion paern in he second year. 3 In fac, i is possible o design exreme examples in which prices increase using one year s consumpion bundle and decrease using he oher. Alhough elaborae echnical mehods allow one o minimize i, his problem is inescapable. Whenever consumpion paerns change, one mus make an arbirary decision abou he composiion of he marke baske, and his decision, unlike he choice of a base year, may affec one s conclusions abou he exen o which prices have changed. The imporance of his problem should no be exaggeraed, however. Consumpion paerns end o change slowly, and sandard price indexes are no unduly affeced by he choice of a consumpion bundle. Moreover, he people who calculae hese indexes have developed reasonable procedures o accoun for gradual changes in consumpion paerns and even for he inroducion of new producs. 4 3 A poin of erminology: An index calculaed wih firs-year quaniies is called a Laspeyres index, and one calculaed wih second-year quaniies is called a Paasche index. 4 For a discussion of hese issues in he case of he CPI, see Charles L. Schulze, op. ci.
7 Table 1. Price Indexes, 1960-2009 CPI Personal Sae and Consumpion Local Gov Deflaor Deflaor (2000=100) (2000=100) Disposable Income Per Capia (curren $) (1982- Year 1984=100) 1960 29.6 20.8 14.7 2,022 1965 31.5 22.1 16.7 2,562 1970 38.8 26.4 22.5 3,586 1975 53.8 36.0 33.5 5,497 1980 82.4 52.1 48.9 8,794 1985 107.6 66.9 64.7 12,911 1990 130.7 80.5 77.4 17,004 1995 152.4 91.6 87.8 20,470 2000 172.2 100.0 100.0 25,994 2001 177.1 102.1 102.9 26,805 2002 179.9 103.5 105.4 27,799 2003 184.0 105.6 109.7 28,805 2004 188.9 108.4 114.4 30,287 2005 195.3 111.6 121.9 31,318 2006 201.6 114.7 128.1 33,157 2007 207.3 117.7 134.7 34,512 2008 215.3 122.0 143.6 35,931 2009 214.5 35,888 2010 218.1 36,691 Source: Annual Repor of he Council of Economic Advisers, Washingon, DC, Governmen Prining Office, 2010. Available ahp://www.gpoaccess.gov/eop/.