Answer Key for Week 3 Homework = 100 = 140 = 138

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1 Econ 110D Fall 2009 K.D. Hoover Answer Key for Week 3 Homework Problem 4.1 a) Laspeyres price index in 2006 = 100 (1 20) + ( ) Laspeyres price index in 2007 = 100 ( ) + (0.5 20) = = 140 Paasche price index in 2006 = 100 (1 30) + ( ) Paasche price index in 2007 = 100 ( ) + (0.5 18) Fisher ideal index in 2006 = = = 138 Fisher ideal index in 2007 = b) Firs calculae chain weighed price index Chain weighed price index in 2006 = 100 Chain weighed price index in 2007 = = 139 Nominal GDP in 2006 = ( ) + ( ) = = 25 Nominal GDP in 2007 = ( ) + ( ) = = 43.5 Real GDP in 2006 (in 2006$) = Real GDP in 2007 (in 2006$) = 43.5 = c) Real GDP in 2006 (in 2007$) = 25 = Real GDP in 2007 (in 2007$) =

2 Problem 4.6 The Laspeyres index suffers from subsiuion bias in which he index will overesimae he magniude of he price increases (i.e. when a price of a goods increases, people will subsiue away for a cheaper goods bu he Laspeyres index keeps he weigh (which is he quaniy) fixed a he base period, causing he index o place oo high a weigh on he price of goods wih relaively higher inflaion. The fixed weigh also makes he Laspeyres index overesimae he magniude of he price increases for oher reason. The Laspeyres index suffers from is inabiliy o capure he in (desirable) qualiy. In some cases, he increase in he price of a produc reflecs he increase in is qualiy (herefore, i is a good hing). The Laspeyres index represens he enire increase in price wihou correcion for any poenial increase in he qualiy. Finally, he Laspeyres index also suffers from new produc bias. I is obvious ha he fixed (quaniy) weigh from he base period (which is in he pas) does no ake ino an accoun he new produc which could represen he significan proporion of he curren consumer expendiures. The Paasche index does no suffer from subsiuion bias (as he Laspeyres index) since is weigh is changing every year. Neverheless, Paasche index suffers from qualiy bias. This happen because when he price of a good rises people will subsiue away for a less desirable (lower qualiy) good. The Paasche index which uses he (quaniy) weigh from he curren period will place oo low a weigh on he price of goods wih relaively higher inflaion. Therefore, he Paasche index will end o underesimae he increase in prices. Mos of he price indices used in he naional accoun in he Unied Saes are based on he chain weighed index. The appealing feaure of he chain weighed index is ha i can be viewed as he (geomeric) average of he Laspeyres and he Paasche index. The chainweighed index overesimaes price less han he Laspeyres index and underesimaes less han he Paasche index. Neverheless, he chain weighed index has an undesirable feaure. Real GDP compued wih a chain weighed index does no always equal o he sum of is componens. This fac also complicaes he analysis ha relies on he conribuion of differen componens in he real GDP (i.e. share in he real GDP). The furher away from he reference period he more misleading his share becomes. 2

3 Problem 4.7 CPI U refers o consumer price index for all urban consumers. The CPI U index for November 2005 is Acual price Year of he acual price CPI U a November of he acual price year Price in November 2005 consan dollars Men s spor coa Coffee (2 lbs.) Ford Sedan (Galaxie) 3, ,431 Reclining chair Washing Machine For example, price of men s spor coa in November 2005 consan dollars (150.16) is calculaed as follows. P reference $ reference X = $ X P $ = $ (Convered prices (las column) are rounded o he same precision as he acual prices(column 2).) Problem 4.8 The GDP price deflaor index for he hird quarer of 1948 is 16.6; for 1980, 54.6; and for 1998, Acual price a he hird quarer of 1998 Price in 1948 consan dollars Price in 1980 consan dollars Vacuum cleaner piece cookware se Man s spor shir Television E machine compuer For example, price of vacuum cleaner 1980 consan dollars (94.14) is calculaed as follows. 3

4 P reference $ reference X = $ X P 54.6 $ = $ (Convered prices (las wo columns) are rounded o he same precision as he acual prices (column 2).) Problem 4.9 The CPI U index for November 1992 is Acual price in 1992 consan dollars (using CPI U) CPI U a November of heir year of sale Price in November of heir year of sale Year of sale One bedroom aparmen (Sacrameno, CA) Men s Neckie Reclining chair Coffee (2 lbs.) Ford sedan (Galaxie) 11, ,997 (Convered prices (las columns) are rounded o he same precision as he acual prices (column 2).) For example, price of one bed aparmen in November of heir year of sale (191.49) is calculaed as follows. P reference $ reference X = $ X P $ = $

5 Problem 5.1 Noe ha he recession period from he NBER below is defined as he period from he quarer a he peak o he quarer a he rough (for example, if he peak is in January and he rough is in July of he same year, he recession is from he firs o he hird quarer of ha year). The following is he comparison of recession period from NBER dae and problem Table 1: Comparison of recession periods from he NBER daes and he wo or more quarers of negaive real GDP growh rule of humb The corresponding Recession period from recession period from NBER problem :4 1949:4 1948:4 1949:2 1953:3 1954:2 1953:2 1954:1 1957:3 1958:2 1957:3 1958:1 1960:2 1961:1 na 1969:4 1970:4 1969:3 1970:1 1973:4 1975:1 1974:2 1975:1 1980:1 1980:3 1980:1 1980:3 1981:3 1982:4 1981:3 1982:1 1990:3 1991:1 1990:2 1991:1 2001:1 2001:4 na 2007:4 2009:1 (ongoing) 2008:2 2009:1 (ongoing) The NBER does no follow he rule of humb as we used in problem Raher he NBER idenifies recession using i) deph as well as duraion in he decline of he economic aciviy (noe ha, he rule of humb solely relies on he duraion of he decline of real GDP) and ii) broader indicaors han only real GDP. Since he rule of humb relies solely on he duraion of he decline in real GDP and does no use any oher indicaor, hese can be reasons of he discrepancy observed in he above able. Also NBER uses monhly daa while our calculaion in problem 2.12 uses quarerly. This can be anoher reason for he discrepancy observed in he above able. For example, if recession sars in March (i.e. in he firs quarer), real GDP for he whole firs quarer migh no show a fall. Our rule of humb would pu he peak a quarer laer han he NBER. 5

6 Problem 5.2 Table 2: Characerisics of he U.S. business cycle since December 1854 (a) Afer 1945 (b) Before 1942 Dae and duraion (in monhs) Dae and duraion (in monhs) Shores recession January 1980 July 1980 Augus 1918 March 1919 (6 monhs) (7 monhs) Shores boom July 1980 July 1981 March 1919 January 1920 (12 monhs) (10 monhs) Shores peak o peak January 1980 July 1981 Augus 1918 January 1920 (18 monhs) (17 monhs) Shores rough o rough July 1980 November 1982 March 1919 July 1921 (28 monhs) (28 monhs) Longes recession July 1981 November 1982 Ocober 1873 March 1879 (16 monhs) (65 monhs) Longes boom March 1991 March 2001 June 1938 Febuary 1945* (120 monhs) (80 monhs) Longes peak o peak July 1990 March 2001 Ocober 1873 March 1882 (128 monhs) (101 monhs) Longes rough o rough March 1991 November 2001 December 1870 March 1879 (128 monhs) (99 monhs) Median recession 10 monhs 18 monhs Median boom 42 monhs 23 monhs Median peak o peak 52.5 monhs 41 monhs Median rough o rough 53.5 monhs 42.5 monhs * If for he period sricly before 1942, he longes boom is March 1933 May 1937 (50 monhs) The curren recession is probably longer han 16 monhs, bu he NBER has no declared he rough ye. (c) The noiceably differen characerisics before 1942 and afer 1945 are as follows 1. The duraion of he boom is longer afer 1945 han This can be seen by he increase in he median boom from 23 monhs (for pre 1942) o 42 monhs (for afer 1945). 2. The duraion of he recession is shorer afer This can be seen by he decrease in he median recession from 18 monhs (for pre 1942) o 10 monhs (for afer 1945). 3. The longes recession is significanly shorer for he period afer 1945 han he period before This can be seen by he reducion of he longes recession from 65 monhs (for pre 1942) o16 monhs (for afer 1945). 4. The duraion of he complee cycle seems o increase afer This can be seen by he increase in he median peak o peak and he median rough o rough from he period pre 1942 o he period afer

7 Problem 5.3 Table 3: Summary of characerisics of he U.S. business cycle based on percenage in real GDP since December 1947 Mean Median Recession series Expansion series Trough o rough series Peak o peak series Table 4: Percenage in real GDP in each recession and expansion since December 1947 Recession Percenage Expansion Percenage 1948:4 1949: :4 1953: :3 1954: :2 1957: :3 1958: :2 1960: :2 1961: :1 1969: :4 1970: :4 1973: :4 1975: :1 1980: :1 1980: :3 1981: :3 1982: :4 1990: :3 1991: :1 2001: :1 2001: :4 2007: Mean Median

8 Table 5: Percenage in real GDP for each complee cycle (each rough o rough and peak o peak) since December 1947 Trough o rough Percenage Peak o peak Percenage 1949:4 1954: :4 1953: :2 1958: :3 1957: :2 1961: :3 1960: :1 1970: :2 1969: :4 1975: :4 1973: :1 1980: :4 1980: :3 1982: :1 1981: :4 1991: :3 1990: :1 2001: :3 2001: :1 2007: Mean Median Problem 5.4 Table 6: Summary of characerisics of he U.S. business cycle based on he in he unemploymen rae since December 1947 Mean Median Recession series Expansion series Trough o rough series Peak o peak series

9 Recession Table 7: Change in he unemploymen rae in each recession and expansion since December 1947 Percenage Expansion Percenage 1948: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Mean Median Table 8: Change in he unemploymen rae for each complee cycle (each rough o rough and peak o peak) since December 1947 Trough o rough Percenage Peak o peak Percenage 1949: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Mean Median

10 Problem 5.5 For he ypical pos World War II business cycle, on average, real GDP falls abou 1.6 percen during he recession while i increases 24.3 percen during he expansion. The unemploymen rae rises, on average, 2.6 percen during he recession while i falls 2.5 percen during he expansion. Noe ha on average he low poins of recessions measured by he rough o rough complee cycles have fallen over ime, he high poins (measured by he in he unemploymen raes over peak o peak complee cycles) have risen. Thus, while we can see ha he unemploymen rae is no perfecly sable, gains in booms more or less offse losses in recessions. Unemploymen raes, of course, end o move in he opposie direcion o real GDP. The ypical recession during pos World War II lass abou 10 monhs (as measured by he median recession) while he expansion lass abou 42 monhs. Far from being symmerical, business cycles are four seps forward and one sep back. Gains o GDP in expansions exceed losses in recessions by more han 13 imes. In he U.S., rend growh overwhelms cyclical flucuaions. For a complee cycle, he real GDP increases, on average, 23 percen. The complee cycle lass abou 53 monhs abou 4½ years (as measured by median peak o peak or median rough o rough). Problem 5.6 Measure recessions by absolue value, hen for example a fall in GDP in a recession of 2 percen would be recorded as 2 percen and no 2 percen. Then he wo correlaions based on he daa in Table 4 above are: 1. correlaion beween he recession and he subsequen expansion = correlaion beween he expansion and subsequen recession = The negaive signs indicae ha large recessions or expansions are associaed wih small subsequen expansions or recessions. And he second correlaion is higher indicaing ha he relaionship is more reliable and consisen ha large expansions are followed by small recessions (or small expansions are followed by large recessions). There are four hypohesis indicaed in he quesion: a) Big expansions are followed by big recessions (and small by small). This suggess ha correlaion #2 should be posiive; bu, in fac, i is negaive; so he evidence is agains i. 10

11 b) Big recessions are followed by big expansions (and small by small). This suggess ha correlaion #1 should be posiive; bu, in fac, i is negaive; so he evidence is agains i. c) Small recessions are followed by big recoveries (and big by small). This suggess ha correlaion #1 should be negaive. I is; so he evidence is consisen wih his hypohesis. However, noice ha correlaion #2 is much bigger han #1. d) Expansions and recessions are essenially uncorrelaed. The fac ha neiher correlaion #1 or #2 is near zero rules his case ou. The quesion also suggesed ha oher hypoheses were possible. The answer o hypohesis c) suggess anoher possibiliy: e) Big expansions are followed by small recessions (and small by big). This suggess ha correlaion #2 should be negaive. I is, so he evidence is consisen wih his hypohesis. Boh hypoheses c) and e) are suppored by he evidence. Noice ha hey are no conradicory. I is perfecly possible ha small recessions are followed by big recoveries and big expansions are followed by small recessions. I suggess ha here could be eiher a viruous spiral (big expansion small recession big expansion small recession...) or a vicious spiral (big recession small expansion big recession small expansion...). We migh hink of he fac ha pos World War II business cycles have been milder and especially ha pos 1982 cycles have been much milder as an example of he viruous spiral. I is an ineresing quesion, wheher he curren large recession is a harbinger of a vicious spiral. The fac ha he correlaions are boh much less han 1, imply ha such spirals are no ineviable, bu may swich from one o he oher. And he fac, ha correlaion #1 is fairly small, suggess ha he swich is mos likely o occur wih a failure of ha relaionship i.e., a case where a small recession is no followed by a big recovery. The recession immediaely before our curren one (2001:1 2001:4) was very mild (in fac, GDP rose slighly!), ye i was no followed by a robus expansion he expansion ha ended December 2007 was only a 17 percen increase in GDP, which is less han he ypical expansions (see Table 3) and less han half of he increase in he previous wo expansions. So, i was an excepion o he correlaion in #1. Le s hope ha here are furher excepions and ha we are no in for a period of a vicious spiral. 11

12 Problem 5.7 Focusing on duraion, he wo correlaions using daa from Table 5.1 are: 1. correlaion beween he recession and he subsequen expansion = correlaion beween he expansion and subsequen recession = The firs correlaion which is posiive indicaes ha long recessions are associaed wih long subsequen expansions. The second correlaion which is negaive indicaes ha long expansions are associaed wih shor subsequen recessions. There are four hypohesis indicaed in he quesion: a) Long expansions are followed by long recessions (and shor by shor). This suggess ha correlaion #2 should be posiive; bu, in fac, i is negaive; so he evidence is agains i. b) Long recessions are followed by long expansions (and shor by shor). This suggess ha correlaion #1 should be posiive; and, in fac, i is posiive; so he evidence is consisen wih his hypohesis. However, noice ha correlaion #2 is much bigger (in absolue value) han #1. c) Shor recessions are followed by long expansions. This suggess ha correlaion #1 should be negaive; bu, in fac, i is posiive; so he evidence is agains i. d) Expansions and recessions are essenially uncorrelaed. The fac ha correlaion #2 is no near zero rules his case ou. The quesion also suggesed ha oher hypoheses were possible. The answer o hypohesis b) suggess anoher possibiliy: e) Long expansions are followed by shor recessions (and shor by long). This suggess ha correlaion #2 should be posiive. The evidence suppors his view. Boh hypohesis b) and hypohesis e) are suppored by he evidence. Though since correlaion #2 is larger han #1 (in absolue value), he link expressed in b) is weaker and less reliable. Bu noice ha b) and c) are no inconsisen wih each oher. One migh have hoped ha he mos recen expansion being above average in lengh migh have been followed by a recession below average as suggesed by e). We do no ye know how long he curren recession will urn ou o be, bu i already appears o be above average and excepion o e) and a harbinger, according o b) of a shorer han ypical subsequen expansion. 12

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