Bài giảng Statistical Techniques in Business and Economics - Chapter 17 Index Numbers

Chapter 17Index NumbersChapter GoalsWhen you have completed this chapter, you will be able to:1.Describe the term index2.Understand the difference between a weighted and an unweighted index3.Construct and interpret a Laspeyres’ price index4.Construct and interpret a Paasche’s price index Construct and interpret a value index 5.Explain how the Consumer Price Index is constructed and interpreted6.TerminologyIndex Number measures the relative change in price, quantity, value, or some other item of interest from one time period to another Simple Index Number measures the relative change in just one variableExampleMr. Wagner owns stock in three companies. Shown below is the price per share at the end of 1996 and 2001 for the three stocks and the quantities he owned in 1996 and 2001Example Stock1996 Price1996 Shares2001 Price2001 SharesNWS$130$250NPC$515$430GAC$640$620ExamplecontinuedStock1996 Price1996 Shares2001 Price2001 SharesNWS$130$250NPC$515$430GAC$640$620Compute a simple price index for each stock. Use 1996 as the base year (1996=100)Simple Price Indexes are:NWS ($2/$1)(100) = 200NPC ($4/$5)(100) = 80GAC ($6/$6)(100) = 100ExamplecontinuedStock1996 Price1996 Shares2001 Price2001 SharesNWS$130$250NPC$515$430GAC$640$620Compute a simple index for the number of shares owned for each. Use 1996 as the base year (1996=100)Simple Shares Indexes are:NWS (50/30)(100) = 166.67NPC (30/15)(100) = 200GAC (20/40)(100) = 50Reasons for computing indexes: they facilitate a comparison of unlike series they are a convenient way to express the change in the total of a heterogeneous group of items they allow for a percent change to be easier to comprehend than actual numbers, especially when the numbers are extremely largeWhy Convert Data to Indexes?Types of Index Numbers*this measures the changes in prices from a selected base period to another period.An index can be classified as a: * price index quantity index, value index or special-purpose indexExamplesTypes of Index NumbersExamplesConsumer Price IndexRetail sales of snowmobiles in Canada the value of eggs sold for consumption in 2000 increased from earlier years? composite www.tse.comprice indexquantity indexvalue indexspecial-purpose indexMore Examples...Types of Index NumbersIndustrial Product Price Indexesmeasure the changes in prices received by Canadian manufacturers for goods as they leave the factory gate. Indirect taxes, transportation, and wholesale and retail costs are not included in the priceRaw Materials Price Indexesmeasure price changes for the purchase of raw materials by Canadian industry. The term “raw material” refers either to a commodity that is sold for the first time after being extracted from nature, or a substitutable recycled productMore Examples... measure changes over time in the contractors’ selling prices of new residential housesTypes of Index NumbersNew Housing Price IndexesMachinery and Equipment Price IndexesNonresidential Building Construction Price IndexesFarm Input Price IndexesFarm Product Price IndexesPrice Indexes of the National Accounts (GDP)othersConstruction of Index NumbersSimple Price Index, P:Let PO be the base period price, and pt be the price at the selected or given period. Thus, the simple price index is given by:Pptpo=(100)A weighted index considers both the price and the quantities of items. There are two methods of computing the price index:Laspeyres method and Paasche methodConstruction of Index NumbersLaspeyresLaspeyres’ Weighted Price Index, P: This method uses the base period quantities as weights.Construction of Index NumbersPpqpqt=SS000(100)Let pt be the current price, p0 be the price in the base period, and q0 be the quantity consumed in the base periodhere the present year weights are substituted for the original base period weights. Let qt be the current quantity consumed, p0 be the price in the base period, and pt be the current price.Paasche’s Weighted Price index, PConstruction of Index NumbersPpqpqttt=SS0(100)here both the price and quantity change from the base period to the given period. A value index reflects changes in both price and quantity:Value indexConstruction of Index NumbersVpqpqtt=SS00(100)Consumer Price IndexIn 1978 two consumer price indexes were published:...one designed for urban wage earners and clerical workersanother designed for all urban householdsUses...CPI allows consumers to determine the effect of price increases on their purchasing power it is a yardstick for revising wages, pensions, alimony payments, etc. it is an economic indicator of the rate of inflation in Canadian it computes real income: real income = money income/CPI(100)Consumer Price IndexUses...Examples...Deflating Sales:Determining the purchasing power of the dollarcompared with its value for the base period:Consumer Price IndexDeflated Sales =Actual SalesAn approximate index (100)Purchasing power of dollar = CPI$1()100Question Determine the purchasing power (PP) of the dollar compared with its value for the base period:PP at the end of the period = 112$54000()100Suppose a person’s income has increased from $44 000 to $54 000 during a 5 year period. Over the same period, the CP has also increased from 100 to 112. What is the real value of the increased income of the person?A= $48 214The real income increase is only $4 214, due to the increase in the cost of living over the 5 yearsWhen two or more series of index numbers are to be compared, they may not have the same base period.Shifting the baseFirst, select a common base period for all series. Then, use the respective base numbers as the denominators and convert each series to the new base period.Stock1996 Price1996 Shares2001 Price2001 SharesNWS$130$250NPC$515$430GAC$640$620From the information given, below perform the following operations: Compute a simple aggregate price index for the three stocks. Stock1996 Price1996 Shares2001 Price2001 SharesNWS$130$250NPC$515$430GAC$640$620Compute a simple aggregate price index for the three stocks. 0.100)100(6$5$1$6$4$2$)100(=++++=SS= 0pp PtUsing LaspeyresComputing the price index using the Laspeyres method35.104)100(345$360$== )100()40(6$)15(5$)30(1$)40(6$)15(4$)30(2$++++= )100(000SS= qpqpPtUsing PaascheComputing the price index using the Paasche method25.106)100(320$340$== )100()20(6$)30(5$)50(1$)20(6$)30(4$)50(2$++++=)100(0SS= tttqpqpPValue IndexComputing the value index55.98)100(345$340$==++)100()40(6$)15(5$)30(1$)20(6$)30(4$)50(2$++=)100(00SS=qpqpPttTest your learning www.mcgrawhill.ca/college/lindClick onOnline Learning Centrefor quizzesextra contentdata setssearchable glossaryaccess to Statistics Canada’s E-Stat dataand much more!This completes Chapter 17