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consumption function for the U.S. economy for the period 1985â€“2019.
1. The residual plots of the interest rate showed a non-random process in the error terms. It looks like
the spread around the mean of the error term is declining with higher interest rates. Include a
residual plot and answer the following questions:
a. How is this problem called? How will it affect the unbiasedness and efficiency of your
b. Please test your model for the problem described in a.. What is the intuition behind the
test you chose? Please explain the process step by step. What is your conclusion?
c. How can you overcome the problem described in a.? Please compare your results to the
results you found without controlling for the problem described in a.? Does your
estimated coefficient change? Does significance of the estimated coefficient change?
2. Your estimator for the interest rate is positive. Some groups found a significant coefficient for the
interest rate; all groups found a positive effect of the interest rate on consumption. This result is
contrary to economic theory. What could be the problem here?
3. The residual plots of Income showed a non-random process in the error terms. After some
research in google and consulting with your econometrics Professor, you found out that this
could be indicative of autocorrelation being present in the error term. You further noticed that
both, Consumption, and Income seem to be growing at a constant rate which might be
indicative of a trend in your data.
a. Describe briefly why ignoring a trend in either the exogenous or the endogenous variables
b. Describe 2 methods to account for a trend in your dataset
c. Your quarterly data of income and consumption (monthly data) appears to show a pattern
within the year. How would you control for that?
4. The residual plot of your model against time indicates that there might be a structural break in your
model.
a. Please indicate the time period where you seem to be able to see the structural break
b. Re-estimate your model and test for a structural break.
c. How would you resolve this issue? Please describe, execute and report your results.
observation_date
Disposable Income
real interest rate 1 year real consumption
1985-01-01
5768.8
4.82351210
5029.959
1985-04-01
5881.0
4.74253160
5076.136
1985-07-01
5862.7
4.27875183
5172.550
1985-10-01
5924.6
4.24991710
5183.741
1986-01-01
6002.5
4.69799443
5229.041
1986-04-01
6079.3
4.85809973
5286.019
1986-07-01
6118.1
3.28548273
5379.527
1986-10-01
6127.4
2.62523037
5412.515
1987-01-01
6183.9
2.68752940
5417.904
1987-04-01
6125.7
2.48904733
5491.837
1987-07-01
6235.5
2.40726957
5554.512
1987-10-01
6319.6
3.16681363
5566.263
1988-01-01
6412.3
2.67632250
5664.593
1988-04-01
6478.4
2.94669133
5706.414
1988-07-01
6540.9
3.03894797
5757.120
1988-10-01
6602.7
3.14464353
5822.579
1989-01-01
6677.8
3.37649407
5849.592
1989-04-01
6658.2
4.33897030
5876.896
1989-07-01
6702.4
3.86855060
5933.790
1989-10-01
6759.2
3.90637900
5959.580
1990-01-01
6811.0
3.87371880
6009.735
1990-04-01
6858.4
4.18567797
6028.041
1990-07-01
6856.1
3.68167533
6051.922
1990-10-01
6797.5
2.24309040
6005.882
1991-01-01
6814.5
2.84223597
5983.298
1991-04-01
6864.4
3.17691737
6032.885
1991-07-01
6892.4
2.73314670
6062.964
1991-10-01
6949.7
1.95482623
6059.930
1992-01-01
7089.5
1.44294417
6173.393
1992-04-01
7159.9
1.49809730
6215.300
1992-07-01
7193.1
1.10201091
6281.923
1992-10-01
7225.7
0.91430723
6356.796
1993-01-01
7252.9
0.75000537
6381.168
1993-04-01
7275.3
0.85743360
6439.211
1993-07-01
7281.6
0.84058137
6510.874
1993-10-01
7332.2
0.73695630
6568.028
1994-01-01
7380.7
0.66690804
6643.151
1994-04-01
7455.0
1.36951563
6694.839
1994-07-01
7498.5
1.83579563
6745.887
1994-10-01
7606.1
2.02862067
6818.819
1995-01-01
7671.0
2.24947053
6835.791
1995-04-01
7692.8
3.06101230
6895.718
1995-07-01
7763.3
2.38563037
6958.210
1995-10-01
7808.7
2.63641577
7006.747
1996-01-01
7882.6
2.38525810
7071.369
1996-04-01
7954.9
2.42318850
7147.441
1996-07-01
8019.3
2.60201713
7190.713
1996-10-01
8062.0
2.32265390
7247.987
1997-01-01
8138.8
2.17722903
7324.388
1997-04-01
8210.9
2.65207710
7357.362
1997-07-01
8307.6
2.80907233
7482.713
1997-10-01
1998-01-01
1998-04-01
1998-07-01
1998-10-01
1999-01-01
1999-04-01
1999-07-01
1999-10-01
2000-01-01
2000-04-01
2000-07-01
2000-10-01
2001-01-01
2001-04-01
2001-07-01
2001-10-01
2002-01-01
2002-04-01
2002-07-01
2002-10-01
2003-01-01
2003-04-01
2003-07-01
2003-10-01
2004-01-01
2004-04-01
2004-07-01
2004-10-01
2005-01-01
2005-04-01
2005-07-01
2005-10-01
2006-01-01
2006-04-01
2006-07-01
2006-10-01
2007-01-01
2007-04-01
2007-07-01
2007-10-01
2008-01-01
2008-04-01
2008-07-01
2008-10-01
2009-01-01
2009-04-01
2009-07-01
2009-10-01
2010-01-01
2010-04-01
2010-07-01
8429.9
8607.4
8725.7
8813.6
8883.4
8980.4
8991.1
9059.8
9181.0
9341.5
9453.0
9575.4
9634.9
9713.4
9688.4
9899.8
9735.4
9963.9
10044.5
10059.5
10123.4
10117.6
10244.6
10424.1
10452.8
10499.2
10608.2
10684.3
10819.2
10688.3
10792.0
10837.1
10928.1
11147.9
11190.4
11212.7
11355.3
11439.4
11491.3
11511.2
11529.3
11548.8
11772.3
11537.5
11662.0
11636.7
11699.3
11557.4
11579.7
11667.4
11860.9
11936.6
2.44497387
2.62856940
2.72494557
2.28409893
2.16714473
2.10610570
2.70443527
2.63098597
2.08955297
2.65081010
2.55431553
3.19865843
2.70722900
3.19237153
1.90213187
1.17941495
0.62769968
0.90776111
0.36150419
0.14081937
-0.17994169
-0.18404371
-0.41644626
0.02025907
-0.32072253
-0.20112586
-0.63716278
-0.75682138
0.30751095
0.48485206
0.65849409
1.44594903
1.10665087
2.46307753
2.25684930
2.36254127
3.20885617
2.28604803
1.53388863
1.94817313
1.79837537
0.68387997
-0.22560473
-1.10238488
2.17588137
2.45034300
0.20863721
-0.98495101
-1.01170224
-1.16592762
-0.44433184
-0.29786953
7572.147
7648.741
7783.430
7884.929
7998.842
8080.996
8204.750
8296.988
8418.349
8545.639
8625.435
8708.074
8784.155
8816.014
8833.726
8864.465
9007.494
9027.548
9073.212
9136.709
9187.527
9232.782
9338.495
9470.541
9535.741
9624.649
9677.166
9790.836
9901.580
9964.496
10074.922
10158.513
10177.238
10288.217
10341.556
10407.966
10507.248
10572.053
10599.795
10670.506
10712.556
10697.867
10727.347
10644.668
10548.872
10522.083
10470.358
10540.769
10529.156
10590.177
10685.145
10761.376
2010-10-01
2011-01-01
2011-04-01
2011-07-01
2011-10-01
2012-01-01
2012-04-01
2012-07-01
2012-10-01
2013-01-01
2013-04-01
2013-07-01
2013-10-01
2014-01-01
2014-04-01
2014-07-01
2014-10-01
2015-01-01
2015-04-01
2015-07-01
2015-10-01
2016-01-01
2016-04-01
2016-07-01
2016-10-01
2017-01-01
2017-04-01
2017-07-01
2017-10-01
2018-01-01
2018-04-01
2018-07-01
2018-10-01
2019-01-01
2019-04-01
2019-07-01
2019-10-01
11980.3
12094.9
12064.1
12117.7
12152.3
12375.7
12486.4
12404.7
12750.9
12248.6
12339.8
12387.2
12424.7
12580.5
12747.1
12890.1
13069.5
13243.4
13280.1
13357.0
13439.8
13541.6
13519.5
13584.8
13656.9
13795.2
13931.9
14015.5
14084.2
14253.3
14373.0
14491.8
14599.1
14729.6
14679.3
14763.1
14850.5
-1.03488270
-1.33853780
-1.87851237
-1.53625992
-1.73031647
-1.52837420
-1.16123002
-1.50045833
-1.89573293
-0.52444344
-0.65569163
-1.03265036
-1.33583117
-1.20694756
-1.34408717
-1.69183160
-1.32109279
1.19416465
-1.00139055
-1.43790663
-0.77173496
-0.29339821
-0.97097101
-1.70712559
-1.92900585
-0.90382333
-0.09542070
-0.61079391
-1.54626170
-0.08816192
0.65689980
-0.30980604
0.13845352
2.28780981
2.27797392
0.66055224
-0.18442748
10827.332
10868.689
10879.873
10912.991
10931.828
11010.694
11030.026
11052.368
11096.365
11155.481
11172.647
11214.417
11304.300
11347.636
11453.014
11565.682
11694.917
11772.949
11852.652
11943.043
12003.146
12091.178
12152.627
12223.822
12283.076
12372.247
12430.081
12500.402
12631.980
12707.641
12816.396
12900.579
12955.501
12975.144
13088.759
13192.261
13248.981
discount rate
8.000
7.770
7.500
7.500
7.367
6.610
5.827
5.500
5.500
5.500
5.650
6.000
6.000
6.000
6.290
6.500
6.697
7.000
7.000
7.000
7.000
7.000
7.000
6.930
6.167
5.660
5.400
4.563
3.500
3.500
3.007
3.000
3.000
3.000
3.000
3.000
3.000
3.247
3.753
4.383
5.083
5.250
5.250
5.250
5.080
5.000
5.000
5.000
5.000
5.000
5.000
5.000
5.000
5.000
5.000
4.663
4.500
4.500
4.603
4.870
5.193
5.737
6.000
6.000
5.110
3.827
3.060
1.643
1.250
1.250
1.250
0.943
2.250
2.167
2.000
2.000
2.000
2.083
2.500
3.000
3.500
4.000
4.500
5.000
5.583
6.000
6.250
6.250
6.250
6.250
5.750
4.917
3.167
2.250
2.250
1.000
0.500
0.500
0.500
0.500
0.667
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.750
0.833
1.000
1.000
1.000
1.083
1.333
1.583
1.750
1.833
2.083
2.333
2.583
2.833
3.000
3.000
2.750
2.250