(a) In taking logarithms of output and consumption, a Federal Reserve economist Anne wrote: "For several reasons, taking logarithms of macroeconomic aggregates is a good ide First, it makes the distributions much closer to the normal distribution, and hence t- and F-statistics are better applicable. Second, a log - log regression allows interpreting the regression coefficient as an elasticity, which is a very useful and intuitive concept in economics and allied disciplines. Even a regression where the dependent variable is in logarithms but the regressor is not provides interpretation in terms of growth rates. Third, and finally, first difference in logarithms is very close to growth rates, and this offers nice interpretation as well." Critically discuss the above statement [10 marks) (b) It is commonly thought that, because of Christmas and holiday spending, 4th quarter consumption expenditure is higher than the first three quarters. Evaluate the validity of the statement on the given data, using analysis of variance. Clearly state your assumptions, null and alternate hypotheses, test statistics and sampling distributions. Discuss the results fully. [15 marks] Office Update To keep up to date with security updates, fixes and ir fx Year A1 E F Nm B C D 1 Year Quarter gdp Icons 2002 1 8.090727405 7.693344439 2002 2 8.12074481 7.72093452 4 2002 3 8.132059982 7.729213877 5 2002 4 8.150086309 7.769002535 6 2003 1 8.114433022 7.717169235 7 2003 2 8.14116416 7.750348662 8 2003 3 8.160887893 7.764183474 2003 4 8.18940026 7.805388232 10 2004 1 8.156672577 7.761059352 11 2004 2 8.182812167 7.784881808 12 2004 3 8.193427879 7.794406261 13 2004 4 8.222503422 7.844228958 14 2005 1 8.190303099 7.792566489 15 2005 2 8.216992014 7.823049915 16 2005 3 8.234528909 7.834903257 17 2005 4 8.251790155 7.874189545 18 2006 1 8.226165529 7.827541096 19 2006 2 8.253569775 7.856307178 20 2006 3 8.252284232 7.859554843 21 2006 4 8.274634633 7.902287343 22 2007 1 8.240737203 7.855593126 23 2007 2 8.268126008 7.878880348 24 2007 3 8.274430946 7.880646358 25 2007 4 8.297485481 7.918891719 26 2008 1 8.26891079 7.87469882 27 2008 2 8.274636417 7.88642871 28 2008 3 8.26790354 7.87350833 29 2008 4 8.26465224 2.891799608 30 2009 1 8.215542004 7.842955691 31 2009 2 8.236355377 7,865876393 32 2009 3 8.24677615 7.870092223 33 2009 4 8.273794125 7.896420252 34 2010 1 8.234644322 7.852717041 35 2010 2 8.265770014 7.883548874 36 2010 3 8.276412771 7887272797 37 2010 4 8.296775172 7.920745407 Sheet A1 x fx Year E A F D B AWNE 1 2 3 4 1 2 3 4 1 2 3 4 38 2011 39 2011 40 2011 41 2011 42 2012 43 2012 44 2012 45 2012 46 2013 47 2013 48 2013 49 2013 50 2014 51 2014 52 2014 53 2014 54 2015 55 2015 56 2015 57 2015 58 2016 59 2016 60 2016 61 2016 62 2017 63 2017 64 2017 65 2017 66 2018 67 2018 68 2018 69 2018 TO 8.258488263 8.28025062 8.286445048 8.310299641 8.28807206 8.302246702 8.310429505 8.32406101 8.295481864 8.316074062 8.331764171 8.353926453 8.313740987 8.340411382 8.360010119 8.379707706 8.346591093 8.377084329 8.386560907 8.397710086 8.36214651 8.389897176 8.400298861 8.417715339 8.375307455 8.411973999 8.425534596 8.444487436 8.40805399 8.44206784 8.452242212 8.473009929 7.876671098 7.904861835 7.903693071 7.93417494 7.896673974 7.919464185 7.914470457 7.948595436 7.901073716 7.930162321 7.9315535 7.97351891 7.920852162 7.957549803 7.96363646 8.009244426 7.960388898 7.997674559 8.000297515 8.039418324 7.989860404 8.023711292 8.026028355 8.06629893 8.011115611 8.050637372 8.050759821 8.093293608 8.03838322 8.077521347 8.079670073 8.12039928 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 (a) In taking logarithms of output and consumption, a Federal Reserve economist Anne wrote: "For several reasons, taking logarithms of macroeconomic aggregates is a good ide First, it makes the distributions much closer to the normal distribution, and hence t- and F-statistics are better applicable. Second, a log - log regression allows interpreting the regression coefficient as an elasticity, which is a very useful and intuitive concept in economics and allied disciplines. Even a regression where the dependent variable is in logarithms but the regressor is not provides interpretation in terms of growth rates. Third, and finally, first difference in logarithms is very close to growth rates, and this offers nice interpretation as well." Critically discuss the above statement [10 marks) (b) It is commonly thought that, because of Christmas and holiday spending, 4th quarter consumption expenditure is higher than the first three quarters. Evaluate the validity of the statement on the given data, using analysis of variance. Clearly state your assumptions, null and alternate hypotheses, test statistics and sampling distributions. Discuss the results fully. [15 marks] Office Update To keep up to date with security updates, fixes and ir fx Year A1 E F Nm B C D 1 Year Quarter gdp Icons 2002 1 8.090727405 7.693344439 2002 2 8.12074481 7.72093452 4 2002 3 8.132059982 7.729213877 5 2002 4 8.150086309 7.769002535 6 2003 1 8.114433022 7.717169235 7 2003 2 8.14116416 7.750348662 8 2003 3 8.160887893 7.764183474 2003 4 8.18940026 7.805388232 10 2004 1 8.156672577 7.761059352 11 2004 2 8.182812167 7.784881808 12 2004 3 8.193427879 7.794406261 13 2004 4 8.222503422 7.844228958 14 2005 1 8.190303099 7.792566489 15 2005 2 8.216992014 7.823049915 16 2005 3 8.234528909 7.834903257 17 2005 4 8.251790155 7.874189545 18 2006 1 8.226165529 7.827541096 19 2006 2 8.253569775 7.856307178 20 2006 3 8.252284232 7.859554843 21 2006 4 8.274634633 7.902287343 22 2007 1 8.240737203 7.855593126 23 2007 2 8.268126008 7.878880348 24 2007 3 8.274430946 7.880646358 25 2007 4 8.297485481 7.918891719 26 2008 1 8.26891079 7.87469882 27 2008 2 8.274636417 7.88642871 28 2008 3 8.26790354 7.87350833 29 2008 4 8.26465224 2.891799608 30 2009 1 8.215542004 7.842955691 31 2009 2 8.236355377 7,865876393 32 2009 3 8.24677615 7.870092223 33 2009 4 8.273794125 7.896420252 34 2010 1 8.234644322 7.852717041 35 2010 2 8.265770014 7.883548874 36 2010 3 8.276412771 7887272797 37 2010 4 8.296775172 7.920745407 Sheet A1 x fx Year E A F D B AWNE 1 2 3 4 1 2 3 4 1 2 3 4 38 2011 39 2011 40 2011 41 2011 42 2012 43 2012 44 2012 45 2012 46 2013 47 2013 48 2013 49 2013 50 2014 51 2014 52 2014 53 2014 54 2015 55 2015 56 2015 57 2015 58 2016 59 2016 60 2016 61 2016 62 2017 63 2017 64 2017 65 2017 66 2018 67 2018 68 2018 69 2018 TO 8.258488263 8.28025062 8.286445048 8.310299641 8.28807206 8.302246702 8.310429505 8.32406101 8.295481864 8.316074062 8.331764171 8.353926453 8.313740987 8.340411382 8.360010119 8.379707706 8.346591093 8.377084329 8.386560907 8.397710086 8.36214651 8.389897176 8.400298861 8.417715339 8.375307455 8.411973999 8.425534596 8.444487436 8.40805399 8.44206784 8.452242212 8.473009929 7.876671098 7.904861835 7.903693071 7.93417494 7.896673974 7.919464185 7.914470457 7.948595436 7.901073716 7.930162321 7.9315535 7.97351891 7.920852162 7.957549803 7.96363646 8.009244426 7.960388898 7.997674559 8.000297515 8.039418324 7.989860404 8.023711292 8.026028355 8.06629893 8.011115611 8.050637372 8.050759821 8.093293608 8.03838322 8.077521347 8.079670073 8.12039928 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
