Supplemen o Chaper 3 I. Measuring Real GD and Inflaion If here were only one good in he world, anchovies, hen daa and prices would deermine real oupu and inflaion perfecly: GD Q ; GD Q. + + + Then, he growh rae of GD, λ, is deermined by: inflaion real growh 678 678 GD + + Q+ + λ + ( + π )( + γ ) GD Q. When more han one good, quaniies and prices of each good are changing a differen raes rying o reduce mulidimensional problem o one dimension. Soluion: Use price and quaniy indices. Calculaion of Real GD Chain weighed calculaion. Use boh presen and preceding year prices o measure value of oupu. Example: GD Year Quaniy rices Anchovies Beer Anchovies Beer 997 4 $0 $5 998 5 3 $2 $5 45; GD $75 λ $75 $45 ( + ). 67 97 $ 98 To measure change in oupu, hold prices consan:
$65 GD in 98 a 97 prices: $ 50 + $5 $65 ( + γ ). 44 $45 This is he simples way o calculae real GD - i uses 997 as he base year. The chain weighed index uses he average of growh implied by using 997 and 998 as base years: $75 $53 GD in 97 a 98 prices: $ 48 + $5 $53 ( + γ ). 45 True growh of real GD is he geomeric average of he wo calculaions: 2 ( + γ ) {( + γ )( + γ )} (.44)(.45). 43 Since he growh of nominal GD is due o real growh and inflaion, he inflaion rae is deermined by: ( ) ( + λ).67 + π.6 ( + γ ).43 (rove his is rue by consrucing a chain-weighed price index: calculae GD in 98 using 97 quaniies, calculae GD in 97 using 98 quaniies. Take geomeric average of implied inflaion raes. his is he GD deflaor. The oher major ype of price index a fixed baske price index Consumer rice Index (CI) Answers he quesion how much would i cos o buy baske of goods a curren prices? Le he base year be denoed, hen he CI in year + is: Discussion: CI + n i n i p p q q i, + i, i, i,. GD deflaor is a broad based index. The implied inflaion rae may no be relevan for households. 2
2. CI oversaes inflaion since i does no permi subsiuion ou of expensive goods. Recen commission chaired by Michael Boskin esimaed ha CI oversaes inflaion rae by % per year. This is no a rivial number since cos of living adjusmens for Social Securiy and oher ransfer programs are ied o his over he nex decade he gov. would save $634 billion dollars. 3. Boh indices do no adjus for qualiy changes. However, since chain weighed indices compare adjacen years, no oo big of a problem. 4. Chain weighed indices are expensive o consruc need annual daa on prices and quaniies. II. Measuring Unemploymen Working Age opulaion Labor Force + No in Labor Force Unemployed (U) Employed (E) No in Labor Force Unemploymen Rae: u U. LF ä The unemploymen rae is affeced by he rae of job separaion (s), he rae of job finding (f), and he movemen of individuals in and ou of he labor force. The Naural Rae of Unemploymen (u*): he unemploymen rae which doesn change. The number of people finding work is equal o he number of people losing work (ignore changes in labor force). Tha is: u * is defined by se fu. 3
Rearranging erms: se or fu s s ( LF U ) ( u *) fu * fu s U LF f U LF Or, s u * s + f. Numerical example: Suppose ha % of he employed lose heir jobs each monh (s 0.0) and 20% of he unemployed find jobs each monh (f 0.20). (These are reasonable numbers: he firs implies ha he average job lass 00 monhs while he average duraion of unemploymen is 5 monhs.) ( 0.0 + 0.20) 0. 0476 u* 0.0 III. Duraion of unemploymen In he US, duraion is characerized by wo facs: F. Mos unemploymen spells are of shor duraion, roughly 2 monhs or less. F2. Mos people who are unemployed on a given dae are experiencing unemploymen spells of long duraion. No conradicory saemens. Example: Labor Force 00. (A) A he beginning of every monh, 2 workers become unemployed and remain unemployed for monh. (A2) A he beginning of every year, 4 workers become unemployed and remain unemployed for he enire year. Over he course of a year, here are 28 spells of unemploymen: 24 spells ha las one monh (A) and 4 spells ha las one year (A2). Thus 24/28 86% of unemploymen spells are of shor duraion -- his is consisen wih F. 4
On a given day afer January, here are six unemployed workers. Two ha have been unemployed for less han one monh and 4 ha have been unemployed for more han a monh. Hence, 4/6 67% of he unemployed are experiencing long spells of unemploymen. -- his is consisen wih F2. IV. Ineres Raes There are many differen ypes of ineres raes he ineres rae on a bond is defined as he yield o mauriy. Bonds are differeniaed by () he issuer and (2) mauriy. We shall be ineresed primarily in: Governmen securiies: Discoun Rae he rae he Fed charges on overnigh loans. Treasury Bills ( 0< M ), Noes (2 M 0), Bonds ( M > 0 ). Ineres raes end o move ogeher bu no always. This was insrumenal in he recen problems wih Long Term Capial Managemen. Difference beween nominal and real ineres raes All bonds are expressed in dollar erms he yields are nominal. You give up curren dollars for he promise of dollars in he fuure. ( + r) ( + r) $ $ + The real ineres rae, ρ, is denominaed in erms of goods. Then, for he above bond, he associaed real ineres rae is: ( + ρ) ( + r) $ $ + + ( + r) + ( + r). ( + π ) Or, approximaely: r ρ + π. If inflaion is uncerain: r ρ + e π. (This is he Fisher relaion). 5
V. Business cycle characerisics In addiion o correlaion and coherence ha are described in Farmer, wo oher feaures of cyclical phenomena are:. Ampliude - he severiy of he cycle. Measured from peak o rough. 2. hase Shif - wheher a variable leads or lags he business cycle (wih he reference variable being GD). Some facs of business cycles: Real Facs: A. Inpu Componens:. Real Wage 2. Labor B. Oupu Componens. Consumer non-durables and services 2. Invesmen and durables consumpion 3. Governmen expendiures Nominal Facs: A. Moneary Aggregaes B. Nominal Ineres raes C. rice Level Coherence hase Shif Ampliude Labor 0 Same Real Wage ** 0 Less Non-durables 0 Much less** Invesmen 0 Much greaer** Governmen very lile corr. M 0/- N/A M2 + (during 80 s) N/A Moneary Base - N/A Nom. Ineres rae - N/A rice Level C** 0 N/A - rocyclical, C - counercyclical. (-, 0, +) -- lags, coinciden, or leads he cycle. 6
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