2. PRICE AND QUANTITY INDICES BUSINESS ECONOMICS, SPRING 2022 PETER JENSEN pje@econ.au.dk LITERATURE: - The Danish Economy: Ch. 11.3.3 - Lequiller & Blades (2014): Ch. 2 - IMF Back to basics – What is inflation? - The Economy – What is wrong with inflation? (Ch. 15.1) LINK 1 TODAY’S LECTURE Price and quantity indices › Comparisons of GDP over time › Quantity indices › Price indices › Inflation › Inflation and interest rates › Inflation and wages 2. PRICE INDICES DESCRIPTIVE ECONOMICS 2 PRICE AND QUANTITY INDICES - INTRODUCTION › Last lecture: Price vs. quantity breakdown › We decomposed nominal GDP into • Quantity changes ο real GDP ο “quantity index” • Price changes ο GDP deflator ο “price index” › This lecture takes a closer look at price indices: 1. Used for the construction of quantity indices by deflating statistics expressed in current prices 2. Are of independent interest as inflation indicators (e.g. CPI = consumer price index) 2. PRICE INDICES DESCRIPTIVE ECONOMICS 3 COMPARING VOLUMES OVER TIME › How exactly do we compute GDP in volume over time? › We deflate nominal GDP using the GDP deflator … › … but how do we obtain the GDP deflator? › The GDP deflator is also called implicit price deflator • is in practice inferred from estimates of nominal GDP and real GDP › Two steps to obtain an estimate of GDP in volume: 1. For each product, derive a statistic expressed in volume 2. Aggregate all products 2. PRICE INDICES DESCRIPTIVE ECONOMICS 4 STEP 1: DERIVING STATISTICS IN VOLUME › To obtain volume statistics of individual products, use one of the following sources a. Statistics expressed in quantities (e.g. tonnes of steel or pork) b. Statistics expressed in current prices (e.g. from company accounts) c. Price indices › Statistics of quantities are rarely available (ca. 20%), so for most products volume statistics are obtained through deflating statistics in current prices by a suitable price index 2. PRICE INDICES DESCRIPTIVE ECONOMICS 5 STEP 2: COMBINING STATISTICS IN VOLUME › How do we add up volume statistics of apples, clothes, haircuts or battle tanks? › We need a common metric: (market) prices › Weighing products by their prices makes economic sense: • Prices reflect relative cost of manufacturing the products • and/or the relative utilities attributed to them by consumers › However, we are interested in change in volume over time… • …prices vary from one year to another › Need to “freeze” prices in one period: Constant-price accounting 2. PRICE INDICES DESCRIPTIVE ECONOMICS 6 QUANTITY INDICES 2. PRICE INDICES DESCRIPTIVE ECONOMICS 7 CONSTANT PRICES: QUANTITY (VOLUME) INDEX › Laspeyres quantity index (using prices of the base year): πΏπΏπΏπΏ πππ‘π‘:0 = Σππ πππππ ×ππππππ Σππ πππππ ×πππππ ππ = 1, … , ππ ππ = ππππππππππ ππ = ππππππππππππππππ › Example: Suppose that the price of the large cars is twice that of the small ones (2 and 1, respectively). Suppose a carmaker produces the same number of cars (=100) in two years, but the proportion of large cars rises from 50% to 80% ο despite total number of cars unchanged, volume increases by 20% πΏπΏπΏπΏ πππ‘π‘:0 = 2∗80+1∗20 2∗50+1∗50 = 180/150 = 1.20 2. PRICE INDICES DESCRIPTIVE ECONOMICS 8 Watch video CONSTANT PRICES: QUANTITY (VOLUME) INDEX › For several years, can derive series of Laspeyres volume indices: Σππ πππππ ×ππππ0 Σππ πππππ ×ππππ1 , , Σππ πππππ ×πππππ Σππ πππππ ×πππππ Σππ πππππ ×ππππ2 , Σππ πππππ ×πππππ › The constant-price series (multiply with Σππ πππππ × πππππ ): …, Σππ πππππ ×πππππ‘π‘ Σππ πππππ ×πππππ Price in t=0 Σππ πππππ × ππππ0 , Σππ πππππ × ππππ1 , Σππ πππππ × ππππ2 , … , Σππ πππππ × πππππ‘π‘ Quantity in t=0 Price in t=1 Quantity in t=1 Price in t=2 Quantity in t=2 Small cars 1 50 1 20 1 10 Large cars 2 50 1.25 80 1.25 100 › Result: • Indices: 1, 1.2, 1.4 • Constant-price series: 150, 180, 210 2. PRICE INDICES DESCRIPTIVE ECONOMICS 9 Watch video BIASES: CHANGE IN RELATIVE PRICES › Weighing by price structure in base period is inaedequate if relative prices change considerably over time › Example: Computers in France • Computers were highly priced compared to equipment GFCF goods in 1980 • Prices for computers fell dramatically in 1980s and 1990s (relative to other equipment) • The fall in prices induced high demand • Using the price structure from 1980 would dramatically overestimate the changes in volume • Solution: chain-linking method 2. PRICE INDICES DESCRIPTIVE ECONOMICS 10 Watch video CHAIN-LINKING METHOD › Chain-linked index (Laspeyres chain) πΏπΏπΏπΏ,πππππππππππππ πΏπΏπΏπΏ πΏπΏπΏπΏ πΏπΏπΏπΏ πΏπΏπΏπΏ = πππ‘π‘:π‘π‘−1 × πππ‘π‘−1:π‘π‘−2 × … × ππ2:1 × ππ1:0 πππ‘π‘:0 › Steps: 1. Continuously update base period: For each year, compute Laspeyres index with previous year as base πΏπΏπΏπΏ year (ο πππ‘π‘:π‘π‘−1 ) πΏπΏπΏπΏ πΏπΏπΏπΏ 2. Link Laspeyres indices (ο πππ‘π‘:π‘π‘−1 × πππ‘π‘−1:π‘π‘−2 × β―) › To obtain series: Multiply by nominal value of base year: Σππ πππππ × πππππ › Example: • t=1: • t=2: Σππ πππππ ×ππππ1 Σππ πππππ ×πππππ Σππ ππππ1 ×ππππ2 Σππ ππππ1 ×ππππ1 ο 1.2 (as before) Σ ππ ×ππ × Σππ πππππ×ππππ1 ο 1.125 × 1.2 = 1.35 < 1.4 ππ πππ πππ • Thus: 1, 1.2, 1.35 • Series: 150, 180, 202.5 2. PRICE INDICES DESCRIPTIVE ECONOMICS 11 Watch video BIASES: NEW PRODUCTS AND QUALITY CHANGE › If new products are introduced in period t=1, which prices do we use in t=0, when the product not yet existed? › ”Hedonic” studies of relationship between price of a good and its key characteristics: • What would have been the price in t=0, had the product existed already back then? • Regarding quality change: What would have been the price in t=0, had new feature already been available back then? › Yields an estimate of unknown value p0 › Example: What would be the price of a self-driving car if this technology was already available today? 2. PRICE INDICES DESCRIPTIVE ECONOMICS 12 PRICE INDICES 2. PRICE INDICES DESCRIPTIVE ECONOMICS 13 PRICE INDICES – EXAMPLE CPI › CPI measures the changes in the prices of consumer goods and services purchased by households National CPI weights, Denmark (2018) › Step 1: selecting the basket Other 27% • Periodic expenditure surveys • Aggregation: weights according to relevance for representative household Services less housing 31% Food and nonalcoholic beverages 12% Energy 8% Housing 22% Source: OECD 2. PRICE INDICES DESCRIPTIVE ECONOMICS 14 EXAMPLE: CPI › Step 2: monthly price survey • 23,000 prices of more than 550 types of goods & services • visit shops, companies and institutions in ca. 1,600 places throughout DK › Step 3: Calculating the price index πΆπΆπΆπΆπΆπΆ = ππππππππ ππππ ππππππππ π¦π¦π¦π¦π¦π¦π¦π¦ ππππππππππππ ππππ ππππππππππππππ ππππππππππππ × 100 ππππππππ ππππππππππππ π¦π¦π¦π¦π¦π¦π¦π¦ ππππππππππππ ππππ ππππππππ ππππππππππππ › The CPI should remind you of the Laspeyres quantity index, except that prices and quantities are interchanged ο This is indeed a Laspeyres price index 2. PRICE INDICES DESCRIPTIVE ECONOMICS 15 LASPEYRES PRICE INDEX › Price indices: fixed basket of ππ goods and services › Laspeyres: use quantities of the base year πΏπΏπΏπΏ πππ‘π‘:0 = Budget method: π΅π΅πππ = Σππ ππππππ ×πππππ Σππ πππππ ×πππππ πΏπΏπΏπΏ πππ‘π‘:0 = Σππ πππππ ×πππππ Σππ πππππ ×πππππ ππππππ πππππ ππ = 1, … , ππ ππ = ππππππππππ ππ = ππππππππππππππππ × π΅π΅πππ π΅π΅πππ = ππππππππππππ π π π π π π π π π ππππππ ππππππππ ππ ππππ π¦π¦π¦π¦π¦π¦π¦π¦ 0 2. PRICE INDICES DESCRIPTIVE ECONOMICS 16 CPI EXAMPLE 2015 2016 Quantity - Bananas 10 0 Price - Bananas €1 €5 Quantity - Oranges 10 10 + 20 = 30 Price - Oranges €1 €1 › CPI: 10∗€5+10∗€1 10∗€1+10∗€1 = 60€ 20€ =3 › Increase in CPI: → 200% (from 1 to 3) › Assumption: consumer is willing to accept 2 oranges for 1 banana › Actual increase in cost of living: 30∗€1 10∗€1+10∗€1 = 30€ 20€ = 1.5 → 50% ο smaller! 2. PRICE INDICES DESCRIPTIVE ECONOMICS 17 SUBSTITUTION BIAS › Prices do not increase uniformly • Price rise more for product A than product B • Product B becomes relatively cheaper ο Consumer substitute product A with B (i.e. shift from A to B) › Laspeyres price index: • Numerator Σππ ππππππ × πππππ : amount needed to afford the old basket at new prices • If consumers take this amount and buy old basket ο equally well off as in base period • But consumers will substitute ο better off than in base period ο numerator Σππ ππππππ × πππππ too large ο Overstates true change in cost of living › This type of bias is analogous to the price structure bias for quantity indices • In both cases, the weights (prices or quantities) becomes distorted relative to the base period › What if we instead use quantities in the final period? 2. PRICE INDICES DESCRIPTIVE ECONOMICS 18 Watch video PAASCHE PRICE INDEX › Use quantities of the current year ππππ πππ‘π‘:0 = Σππ ππππππ ×ππππππ Σππ πππππ ×ππππππ › Paasche price index in bananas/oranges example? (Result: 0% increase) › Paasche price index: • Denominator Σππ πππππ × ππππππ : amount needed to afford the new basket at old prices • If consumers take this amount and buy new basket ο equally well off as in final period • But consumers will substitute ο better off than in final period ο denominator Σππ πππππ × ππππππ too large ο Understates true change in cost of living 2. PRICE INDICES DESCRIPTIVE ECONOMICS 19 Watch video SUBSTITUTION BIAS › It follows: πΏπΏπ΄π΄ πππ΄π΄ πΏπΏπ΄π΄ πππ΄π΄ πππ‘π‘:0 > π‘π‘π‘π‘π‘π‘π‘π‘ πππππππππππ ππππ ππππππππ ππππ ππππππππππππ > πππ‘π‘:0 ⇒ πππ‘π‘:0 > πππ‘π‘:0 › Remedy: Fisher index = geometric mean of Laspeyres and Paasche indices › Example: See also book, Ch. 11.3.3 (page 294) πΉπΉ πππ‘π‘:0 = ππππ πΏπΏπΏπΏ πππ‘π‘:0 × πππ‘π‘:0 πππΉπΉ = 124 × 119 = 121.5 2. PRICE INDICES DESCRIPTIVE ECONOMICS 20 Watch video QUALITY/NEW PRODUCT BIAS › Quality (example: laptops) • Improves over time for same product • Better quality increases consumer’s well-being • Price increase partly reflects quality increase ο Increase in cost of living overstated › New products (example: iPad in 2010): • Not included in fixed basket index or with some delay • Increase well-being (otherwise consumers would continue buying old products) ο Increase in cost of living overstated › Boskin Report (1996): CPI overstates US inflation by 1.1%-points › 0.4%-points due to substitution bias › 0.6%-points due to introduction of new products/quality change › 0.1%-points due to growth of discount stores (outlet bias) 2. PRICE INDICES DESCRIPTIVE ECONOMICS 21 RECAP: CPI VS. GDP DEFLATOR › CPI: • prices of › consumer goods and services purchased by households › no matter whether produced domestically or imported • Laspeyres index › GDP deflator: • price › all goods and services goods (including also e.g. military spending, machines, trucks etc.) › produced domestically • Paasche index 2. PRICE INDICES DESCRIPTIVE ECONOMICS 22 INFLATION 2. PRICE INDICES DESCRIPTIVE ECONOMICS 23 WHAT IS INFLATION AND WHY DO WE CARE ABOUT IT? Deutsche Welle, January 6, 2022; LINK 2. PRICE INDICES DESCRIPTIVE ECONOMICS 24 HARMONISED INDEX OF CONSUMER PRICES (HICP) • compiled by EU member states (and Norway, Iceland and Switzerland) • enables comparability across European countries • HICP basket is updated on an annual basis to include new products that have become an important part of household consumption expenditure • Aims at measuring “pure” price changes over time: quality adjustment • used by European Central Bank as target for monetary policy: “HICP inflation rate of below 2% over the medium term” • only difference with Danish CPI: owner-occupied dwellings are not included • ”Core HICP”: excludes goods with › highly volatile prices (= temporary changes in prices): energy, food › administered prices (= deliberate changes in prices): alcohol, tobacco 2. PRICE INDICES DESCRIPTIVE ECONOMICS 25 CONSUMER PRICE INDICES - DENMARK Various inflation indicators for Denmark - Annual change in January 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 1997 -0,5 1999 2001 2003 CPI Source: Eurostat/Statistics Denmark 2005 HICP 2007 2009 2011 2013 2015 Core HICPI 2. PRICE INDICES DESCRIPTIVE ECONOMICS 26 -1,00 1999Jan 1999Jul 2000Jan 2000Jul 2001Jan 2001Jul 2002Jan 2002Jul 2003Jan 2003Jul 2004Jan 2004Jul 2005Jan 2005Jul 2006Jan 2006Jul 2007Jan 2007Jul 2008Jan 2008Jul 2009Jan 2009Jul 2010Jan 2010Jul 2011Jan 2011Jul 2012Jan 2012Jul 2013Jan 2013Jul 2014Jan 2014Jul 2015Jan 2015Jul 2016Jan ECB TARGET AND EURO AREA HCPI HCPI Euro Area - Monthly index, Year-to-Year %-change - 5,00 4,00 3,00 2,00 1,00 0,00 -2,00 HCPI Euro Area Source: ECB ECB target (2%) 2. PRICE INDICES DESCRIPTIVE ECONOMICS 27 Watch video COST AND BENEFITS OF INFLATION › Inflation has redistributive effects: • Borrowers with nominal debt will benefit › Loans/mortgages with nominal interest rate will benefit because the debt stays the same in nominal terms, but becomes smaller in real terms • Lenders with nominal assets will lose › Banks or others who have loaned money at fixed nominal interest rates will lose because when the sum is repaid it will be worth less in terms of the goods or services it can buy › Example: You want to buy a new laptop in a year from now (price today: 10,500 DKK). You expect zero inflation. A Danish government bond yields 5% interest per year. • How much do you invest today? 10,500 DKK / 1.05 = 10,000 DKK. • Assume prices unexpectedly increase by 2%. Price of laptop will be 10,710 DKK • But you only have 10,500 DKK ο Interest payment is too low to afford laptop ο Real interest rate of the bond was smaller than 5% 2. PRICE INDICES DESCRIPTIVE ECONOMICS 28 Watch video DERIVING THE REAL INTEREST RATE › In analogy to GDP equation: 1 + ππππππππππππππ ππππππππππππππππ ππππππππ = 1 + ππππππππ ππππππππππππππππ ππππππππ ∗ 1 + ππππππππππππππππππ → 1 + ππππππππ ππππππππππππππππ ππππππππ = 1 + ππππππππππππππ ππππππππππππππππ ππππππππ ⁄ 1 + ππππππππππππππππππ › Plugging in values and solving yields a real interest rate = 2.94% › Alternative calculation: › Use approximation ππππ 1 + π₯π₯ ≈ π₯π₯ 1 + ππππππππ ππππππππππππππππ ππππππππ = 1 + ππππππππππππππ ππππππππππππππππ ππππππππ ⁄ 1 + ππππππππππππππππππ ln 1 + ππππππππ ππππππππππππππππ ππππππππ = ππππ 1 + ππππππππππππππ ππππππππππππππππ ππππππππ − ππππ 1 + ππππππππππππππππππ → ππππππππ ππππππππππππππππ ππππππππ = ππππππππππππππ ππππππππππππππππ ππππππππ − ππππππππππππππππππ › Here: 5% - 2% = 3% › You might have 10,500 DKK after a year, but this amount is only worth 10,294 DKK (or approximately 10,300 DKK) in today’s prices ο not enough to buy laptop because < 10,500 DKK 2. PRICE INDICES DESCRIPTIVE ECONOMICS 29 -2 -4 Jan-1987 Dec-1987 Nov-1988 Oct-1989 Sep-1990 Aug-1991 Jul-1992 Jun-1993 May-1994 Apr-1995 Mar-1996 Feb-1997 Jan-1998 Dec-1998 Nov-1999 Oct-2000 Sep-2001 Aug-2002 Jul-2003 Jun-2004 May-2005 Apr-2006 Mar-2007 Feb-2008 Jan-2009 Dec-2009 Nov-2010 Oct-2011 Sep-2012 Aug-2013 Jul-2014 Jun-2015 Watch video NOMINAL VS. REAL INTEREST RATES Nominal and real interest rates in Denmark 14 12 10 8 6 4 2 0 Long-term government bond interest rate Real interest rate (corrected for CPI) Source: OECD 2. PRICE INDICES DESCRIPTIVE ECONOMICS 30 Watch video COST AND BENEFITS OF INFLATION › Wages: • Working contracts specify wage increases for several years in advance • Often incorporate compensations for future inflation • However: unexpected inflation lowers real value of wages ο bad for workers, good for employers • What is the real values of wages? › Need to deflate nominal wages with price index › Choose appropriate price index (consumption basket of workers possibly dependent on industry) • Nominal vs. real wages 2. PRICE INDICES DESCRIPTIVE ECONOMICS 31 Watch video DEFLATING NOMINAL WAGES › Only few variables are typically available as both value and quantity indices, e.g. GDP › Often, we only know the value index ο need to deflate it with appropriate price index › Similar calculation as before: • (1 + growth of real wages) = (1 + growth of wage index)/(1 + growth of CPI) › Interpretation: Purchasing power of wages (“real wages”) increased by 0.3% › here the approximation gives the same result: 7%-6.7% = 0.3% . Wage index for manufacturing 2005:Q1=100 2010=100 Consumer price index (CPI): 2000=100 2010=100 Index of real wages (quantity index): 2010=100 2010 2014 120.1 100 128.5 107.0 122.4 100 130.6 106.7 100 100.3 Source: Danish Economy, Chapter 11.3.3 2. PRICE INDICES DESCRIPTIVE ECONOMICS 32 Watch video CPI VS. NOMINAL WAGES CPI vs. Average Earnings in Corporations and Organizations in Denmark - Annual % changes 5,0 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 Average earnings CPI Source: Statistics Denmark 2. PRICE INDICES DESCRIPTIVE ECONOMICS 33 COST AND BENEFITS OF INFLATION › Cost: • menu costs: frequent updates of prices (e.g. restaurant menu) • In an environment with high and volatile inflation, prices no longer signal relative scarcity of resources accurately ο distorts investment and consumption decisions › Benefits: • anticipation of slightly higher prices in the future gives consumers an incentive to make purchase now rather than later ο boosts economic activity • conversely: deflation leads consumers to delay purchases ο hampers economic activity (e.g. Japan 1995-2015) • In a dynamic economy with declining sectors, real wages sometimes need to go down to avoid unemployment, but nominal wages are downward-rigid (workers are unwilling to accept nominal wage cuts) ο only way to achieve real wage cuts is by inflation (“Inflation greases the wheels of the labour market”) ο Most central banks aim at low and predictable inflation - “inflation targeting” ECB: 2% 2. PRICE INDICES DESCRIPTIVE ECONOMICS 34 HYPERINFLATION IN GERMANY 1923 2. PRICE INDICES DESCRIPTIVE ECONOMICS 35 RECENT EXAMPLES OF HYPERINFLATION 2008 2. PRICE INDICES DESCRIPTIVE ECONOMICS 36 LINK 2. PRICE INDICES DESCRIPTIVE ECONOMICS 37 TODAY’S LECTURE - SUMMARY › Key concepts: Laspeyres index Paasche index Inflation Real interest rate, real wage › Key points: To compare economic figures over time, we need to adjust for price changes Price indices can overstate (Laspeyres) or understate (Paasche) the true change in cost of living Inflation has both costs and benefits → target values 2. PRICE INDICES DESCRIPTIVE ECONOMICS 38
