Question

Part 2: Transforming data and computing descriptive statistics

Create a quarterly real GDP series by dividing nominal GDP by the GDP deflator. Also, create a money velocity series as PY/M where P is the price level, Y is real GDP, and M is the M3 money supply measure.

a. Plot the velocity of money (produce a graph similar to Figure 8.2 on page 212 of the textbook). Has velocity risen or fallen over the sample period? b. What is the mean and standard deviation of M3 velocity?

picture from textbook: https://media.cheggcdn.com/media%2Fb3d%2Fb3d56712-5053-405f-83e0-88009e1d6240%2FphpGAezM0.png

data to be used:

observation_date	MABMM301CAQ189S		observation_date	CANGDPDEFQISMEI		Quarterly	v62295562 - Gross domestic product at market prices (x 1,000,000)
1981-01-01	2.04311E+11		1981-01-01	42.69811116		Q1 1981	354,784
1981-04-01	2.07984E+11		1981-04-01	43.66104146		Q2 1981	366,788
1981-07-01	2.16848E+11		1981-07-01	44.62899825		Q3 1981	371,560
1981-10-01	2.18082E+11		1981-10-01	45.29084386		Q4 1981	375,352
1982-01-01	2.17479E+11		1982-01-01	46.60831697		Q1 1982	381,676
1982-04-01	2.19886E+11		1982-04-01	47.57980057		Q2 1982	385,140
1982-07-01	2.2233E+11		1982-07-01	48.37395895		Q3 1982	388,116
1982-10-01	2.24304E+11		1982-10-01	49.3332838		Q4 1982	392,160
1983-01-01	2.2614E+11		1983-01-01	49.71327644		Q1 1983	401,680
1983-04-01	2.24478E+11		1983-04-01	50.26292877		Q2 1983	414,192
1983-07-01	2.25279E+11		1983-07-01	51.27358864		Q3 1983	427,308
1983-10-01	2.27179E+11		1983-10-01	51.61005878		Q4 1983	435,584
1984-01-01	2.283E+11		1984-01-01	51.97043324		Q1 1984	446,148
1984-04-01	2.32617E+11		1984-04-01	52.30782428		Q2 1984	457,828
1984-07-01	2.37141E+11		1984-07-01	52.72343939		Q3 1984	463,424
1984-10-01	2.40677E+11		1984-10-01	53.04197052		Q4 1984	473,572
1985-01-01	2.44981E+11		1985-01-01	53.42486468		Q1 1985	484,236
1985-04-01	2.48915E+11		1985-04-01	54.26513634		Q2 1985	493,432
1985-07-01	2.5245E+11		1985-07-01	54.50504061		Q3 1985	501,888
1985-10-01	2.5701E+11		1985-10-01	54.84025435		Q4 1985	512,744
1986-01-01	2.64237E+11		1986-01-01	55.25634718		Q1 1986	516,520
1986-04-01	2.68411E+11		1986-04-01	55.49059389		Q2 1986	521,696
1986-07-01	2.71948E+11		1986-07-01	56.09128688		Q3 1986	528,016
1986-10-01	2.8153E+11		1986-10-01	56.87836721		Q4 1986	531,568
1987-01-01	2.91177E+11		1987-01-01	57.53317263		Q1 1987	550,140
1987-04-01	2.99965E+11		1987-04-01	58.33295861		Q2 1987	565,020
1987-07-01	3.05585E+11		1987-07-01	58.89916591		Q3 1987	579,244
1987-10-01	3.08066E+11		1987-10-01	59.55513344		Q4 1987	593,300
1988-01-01	3.12459E+11		1988-01-01	60.19836959		Q1 1988	608,480
1988-04-01	3.22487E+11		1988-04-01	60.66882712		Q2 1988	618,684
1988-07-01	3.34801E+11		1988-07-01	61.66399317		Q3 1988	628,884
1988-10-01	3.42958E+11		1988-10-01	62.46758329		Q4 1988	641,556
1989-01-01	3.51835E+11		1989-01-01	62.92301878		Q1 1989	653,604
1989-04-01	3.62677E+11		1989-04-01	63.98918575		Q2 1989	667,232
1989-07-01	3.73418E+11		1989-07-01	64.65157352		Q3 1989	676,572
1989-10-01	3.85482E+11		1989-10-01	64.99380354		Q4 1989	678,696
1990-01-01	3.95554E+11		1990-01-01	65.40531748		Q1 1990	689,404
1990-04-01	4.0366E+11		1990-04-01	66.03354097		Q2 1990	693,132
1990-07-01	4.10993E+11		1990-07-01	66.70745429		Q3 1990	695,180
1990-10-01	4.1872E+11		1990-10-01	67.22290923		Q4 1990	694,272
1991-01-01	4.27352E+11		1991-01-01	67.93588676		Q1 1991	691,484
1991-04-01	4.32806E+11		1991-04-01	68.36517541		Q2 1991	699,036
1991-07-01	4.33277E+11		1991-07-01	68.59406171		Q3 1991	702,272
1991-10-01	4.39453E+11		1991-10-01	68.66059067		Q4 1991	704,220
1992-01-01	4.45823E+11		1992-01-01	68.94091388		Q1 1992	707,560
1992-04-01	4.50337E+11		1992-04-01	69.32202186		Q2 1992	712,328
1992-07-01	4.57429E+11		1992-07-01	69.62116203		Q3 1992	719,252
1992-10-01	4.64677E+11		1992-10-01	69.77651809		Q4 1992	724,936
1993-01-01	4.70009E+11		1993-01-01	69.96565871		Q1 1993	731,528
1993-04-01	4.72942E+11		1993-04-01	70.41575784		Q2 1993	742,932
1993-07-01	4.75799E+11		1993-07-01	70.19167988		Q3 1993	747,640
1993-10-01	4.79652E+11		1993-10-01	70.70364286		Q4 1993	756,332
1994-01-01	4.8357E+11		1994-01-01	70.95633662		Q1 1994	770,204
1994-04-01	4.89883E+11		1994-04-01	70.93029423		Q2 1994	781,204
1994-07-01	5.00109E+11		1994-07-01	71.5711307		Q3 1994	798,332
1994-10-01	5.03525E+11		1994-10-01	71.94169718		Q4 1994	808,288
1995-01-01	5.07562E+11		1995-01-01	72.43909165		Q1 1995	821,384
1995-04-01	5.15417E+11		1995-04-01	72.8401001		Q2 1995	826,212
1995-07-01	5.24551E+11		1995-07-01	73.10778253		Q3 1995	830,332
1995-10-01	5.29711E+11		1995-10-01	73.48182065		Q4 1995	837,964
1996-01-01	5.39297E+11		1996-01-01	73.73975025		Q1 1996	841,428
1996-04-01	5.45922E+11		1996-04-01	73.98403847		Q2 1996	850,092
1996-07-01	5.50767E+11		1996-07-01	74.34930978		Q3 1996	861,784
1996-10-01	5.55781E+11		1996-10-01	74.87572976		Q4 1996	874,788
1997-01-01	5.65662E+11		1997-01-01	75.08368347		Q1 1997	888,792
1997-04-01	5.70634E+11		1997-04-01	74.88081067		Q2 1997	896,372
1997-07-01	5.75825E+11		1997-07-01	75.08607625		Q3 1997	909,568
1997-10-01	5.85016E+11		1997-10-01	75.29788696		Q4 1997	920,876
1998-01-01	5.88563E+11		1998-01-01	75.10463509		Q1 1998	931,392
1998-04-01	5.92121E+11		1998-04-01	75.11357127		Q2 1998	931,908
1998-07-01	5.97459E+11		1998-07-01	74.72571561		Q3 1998	935,696
1998-10-01	6.02599E+11		1998-10-01	74.87131258		Q4 1998	950,184
1999-01-01	6.02129E+11		1999-01-01	75.21325796		Q1 1999	971,824
1999-04-01	6.13187E+11		1999-04-01	76.03927032		Q2 1999	990,748
1999-07-01	6.21062E+11		1999-07-01	76.91249304		Q3 1999	1,017,736
1999-10-01	6.32911E+11		1999-10-01	77.30843557		Q4 1999	1,037,516
2000-01-01	6.48037E+11		2000-01-01	78.22530767		Q1 2000	1,066,576
2000-04-01	6.58564E+11		2000-04-01	79.42312702		Q2 2000	1,095,808
2000-07-01	6.74681E+11		2000-07-01	80.21978873		Q3 2000	1,117,980
2000-10-01	6.83844E+11		2000-10-01	80.87774982		Q4 2000	1,129,156
2001-01-01	6.93689E+11		2001-01-01	81.65841791		Q1 2001	1,145,988
2001-04-01	6.96378E+11		2001-04-01	81.65117527		Q2 2001	1,148,844
2001-07-01	7.0454E+11		2001-07-01	80.70759895		Q3 2001	1,134,708
2001-10-01	7.1682E+11		2001-10-01	80.0583262		Q4 2001	1,132,480
2002-01-01	7.29263E+11		2002-01-01	80.41861287		Q1 2002	1,154,524
2002-04-01	7.34895E+11		2002-04-01	81.83423125		Q2 2002	1,181,544
2002-07-01	7.50367E+11		2002-07-01	82.38631683		Q3 2002	1,199,908
2002-10-01	7.58437E+11		2002-10-01	83.42950962		Q4 2002	1,221,832
2003-01-01	7.61874E+11		2003-01-01	84.59159619		Q1 2003	1,245,676
2003-04-01	7.82063E+11		2003-04-01	83.87561141		Q2 2003	1,233,300
2003-07-01	7.96029E+11		2003-07-01	84.95635352		Q3 2003	1,253,900
2003-10-01	8.07003E+11		2003-10-01	85.3524376		Q4 2003	1,268,384
2004-01-01	8.30867E+11		2004-01-01	86.29841734		Q1 2004	1,291,688
2004-04-01	8.50393E+11		2004-04-01	87.39335372		Q2 2004	1,323,544
2004-07-01	8.63961E+11		2004-07-01	87.89404677		Q3 2004	1,346,952
2004-10-01	8.85819E+11		2004-10-01	88.27669893		Q4 2004	1,362,528
2005-01-01	9.14545E+11		2005-01-01	88.82847112		Q1 2005	1,375,720
2005-04-01	9.38963E+11		2005-04-01	89.42817592		Q2 2005	1,394,868
2005-07-01	9.54247E+11		2005-07-01	90.72483988		Q3 2005	1,432,508
2005-10-01	9.62155E+11		2005-10-01	91.87374486		Q4 2005	1,465,016
2006-01-01	9.81505E+11		2006-01-01	91.54859597		Q1 2006	1,471,532
2006-04-01	9.99682E+11		2006-04-01	92.42400195		Q2 2006	1,486,320
2006-07-01	1.02234E+12		2006-07-01	93.05784619		Q3 2006	1,500,672
2006-10-01	1.04904E+12		2006-10-01	93.3031751		Q4 2006	1,510,304
2007-01-01	1.07602E+12		2007-01-01	94.71213816		Q1 2007	1,543,024
2007-04-01	1.10249E+12		2007-04-01	95.59095835		Q2 2007	1,572,372
2007-07-01	1.14279E+12		2007-07-01	95.53638302		Q3 2007	1,578,004
2007-10-01	1.17806E+12		2007-10-01	96.77660407		Q4 2007	1,600,728
2008-01-01	1.21117E+12		2008-01-01	98.67959821		Q1 2008	1,633,172
2008-04-01	1.25192E+12		2008-04-01	100.7423479		Q2 2008	1,673,096
2008-07-01	1.28028E+12		2008-07-01	100.9439217		Q3 2008	1,690,428
2008-10-01	1.30447E+12		2008-10-01	97.56793201		Q4 2008	1,614,996
2009-01-01	1.29867E+12		2009-01-01	96.02749385		Q1 2009	1,553,180
2009-04-01	1.29828E+12		2009-04-01	96.54850348		Q2 2009	1,544,376
2009-07-01	1.3059E+12		2009-07-01	97.33262931		Q3 2009	1,563,964
2009-10-01	1.31498E+12		2009-10-01	98.90114935		Q4 2009	1,607,940
2010-01-01	1.32874E+12		2010-01-01	99.68889426		Q1 2010	1,640,056
2010-04-01	1.36292E+12		2010-04-01	99.73092225		Q2 2010	1,649,184
2010-07-01	1.39202E+12		2010-07-01	99.76256572		Q3 2010	1,661,488
2010-10-01	1.40577E+12		2010-10-01	100.8028477		Q4 2010	1,697,792
2011-01-01	1.43135E+12		2011-01-01	102.1875932		Q1 2011	1,733,840
2011-04-01	1.45784E+12		2011-04-01	103.2762484		Q2 2011	1,755,640
2011-07-01	1.48928E+12		2011-07-01	103.3687047		Q3 2011	1,781,600
2011-10-01	1.52151E+12		2011-10-01	104.1128451		Q4 2011	1,808,604
2012-01-01	1.55116E+12		2012-01-01	104.2014187		Q1 2012	1,810,720
2012-04-01	1.57589E+12		2012-04-01	104.0827415		Q2 2012	1,814,628
2012-07-01	1.59536E+12		2012-07-01	104.5453546		Q3 2012	1,826,288
2012-10-01	1.61098E+12		2012-10-01	105.1788905		Q4 2012	1,839,596
2013-01-01	1.63607E+12		2013-01-01	105.9475736		Q1 2013	1,872,136
2013-04-01	1.67053E+12		2013-04-01	105.8155098		Q2 2013	1,881,924
2013-07-01	1.69833E+12		2013-07-01	106.3926058		Q3 2013	1,907,692
2013-10-01	1.75066E+12		2013-10-01	106.4727711		Q4 2013	1,928,372
2014-01-01	1.78916E+12		2014-01-01	108.0058207		Q1 2014	1,958,572
2014-04-01	1.81251E+12		2014-04-01	108.0948485		Q2 2014	1,983,684
2014-07-01	1.85501E+12		2014-07-01	108.6916969		Q3 2014	2,009,164
2014-10-01	1.89181E+12		2014-10-01	108.2081793		Q4 2014	2,009,312
2015-01-01	1.92827E+12		2015-01-01	107.1608189		Q1 2015	1,985,880
2015-04-01	1.95461E+12		2015-04-01	107.4289334		Q2 2015	1,987,968
2015-07-01	2.01857E+12		2015-07-01	107.7699516		Q3 2015	2,005,556
2015-10-01	2.05577E+12		2015-10-01	107.3727069		Q4 2015	2,000,240
2016-01-01	2.09906E+12		2016-01-01	107.1804261		Q1 2016	2,008,964
2016-04-01	2.14464E+12		2016-04-01	107.4862374		Q2 2016	2,009,416
2016-07-01	2.19735E+12		2016-07-01	108.2285573		Q3 2016	2,044,564
2016-10-01	2.2347E+12		2016-10-01	109.4481763		Q4 2016	2,079,080
2017-01-01	2.25137E+12		2017-01-01	110.2520312		Q1 2017	2,115,064
2017-04-01	2.30112E+12		2017-04-01	110.1958834		Q2 2017	2,136,712
2017-07-01	2.29036E+12		2017-07-01	110.2431625		Q3 2017

Answer 1

A. REAL GDP AND MONEY VELOCITY CALCULATED IN THE TABLE (JUST FEW ROWS AS I WAS UNABLE TO PASTE ENTIRE EXCEL)

observation_date	MABMM301CAQ189S (M)	CANGDPDEFQISMEI : GDP DEFLATOR (P)	Quarterly	v62295562 - Gross domestic product at market prices (x 1,000,000) (NOMINAL GDP)	Real gdp (G ): Y = NOMINAL GDP/ GDP DEFLATOR	money velocity series as PY/M	sunstracting money velocity from mean (1.53) = U	U2 = square of U
1/1/1981	2.04E+11	42.69811116	Q1 1981	354,784	8,309,126,337	1.74	0.21	0.04
4/1/1981	2.08E+11	43.66104146	Q2 1981	366,788	8,400,807,396	1.76	0.23	0.05
7/1/1981	2.17E+11	44.62899825	Q3 1981	371,560	8,325,528,570	1.71	0.18	0.03
10/1/1981	2.18E+11	45.29084386	Q4 1981	375,352	8,287,591,222	1.72	0.19	0.04
1/1/1982	2.17E+11	46.60831697	Q1 1982	381,676	8,189,010,563	1.76	0.23	0.05
4/1/1982	2.20E+11	47.57980057	Q2 1982	385,140	8,094,611,482	1.75	0.22	0.05
7/1/1982	2.22E+11	48.37395895	Q3 1982	388,116	8,023,242,431	1.75	0.22	0.05
10/1/1982	2.24E+11	49.3332838	Q4 1982	392,160	7,949,197,171	1.75	0.22	0.05
1/1/1983	2.26E+11	49.71327644	Q1 1983	401,680	8,079,934,150	1.78	0.25	0.06
4/1/1983	2.24E+11	50.26292877	Q2 1983	414,192	8,240,506,674	1.85	0.32	0.10
7/1/1983	2.25E+11	51.27358864	Q3 1983	427,308	8,333,881,270	1.90	0.37	0.13

B. VELOCITY OF MENOY HAS BEEN PLOTTED IN THE GRAPH. Money velocity has definitely fallen over the chart period from 1.7 (in 1980s) to 0.9 (in 2017).

Mean of velocity is: average = sum of all obcervations/number of observations = 223.69/146 = 1.53

Standard deviation of M3 velocity = square root of [{ sum of (all observations – average mean)² }/number of observations]

à in above table, std deviation= square root of [(sum of U2)/146] à square root {11.69/146} à

square root (0.08) à 0.2828