Year CR C Y 1945 6800 85.865 10516 1946 9777 101.369 10289 1947 13298 112.357 96
ID: 1139391 • Letter: Y
Question
Year CR C Y
1945 6800 85.865 10516
1946 9777 101.369 10289
1947 13298 112.357 9684
1948 16332 122.175 10019
1949 19374 126.69 9927
1950 23947 138.416 10666
1951 25350 148.955 10839
1952 30522 156.563 11026
1953 34614 168.057 11368
1954 35963 172.661 11330
1955 42949 188.323 11873
1956 46580 197.574 12223
1957 49217 208.377 12317
1958 49490 214.014 12241
1959 57213 232.564 12560
1960 61248 244.446 12629
1961 63435 253.137 12861
1962 69344 272.105 13281
1963 77870 289.325 13585
1964 87352 313.028 14350
1965 97489 338.47 15052
1966 103422 367.099 15672
1967 108567 389.997 16181
1968 119324 431.788 16748
1969 129231 469.283 17148
1970 133660 501.714 17734
1971 149243 548.468 18321
1972 168757 605.844 18999
1973 192980 668.477 19989
1974 201926 719.66 19583
1975 206996 797.314 19869
1976 228961 894.732 20306
1977 264892 998.604 20740
1978 311305 1122.434 21455
1979 354616 1239.694 21630
1980 358044 1353.099 21542
1981 377882 1501.523 21849
1982 396718 1622.935 22113
1983 444878 1817.221 22669
1984 526584 2008.148 24016
1985 610574 2210.337 24518
1986 666355 2391.294 25219
1987 698640 2566.614 25548
1988 745206 2793.129 26508
1989 809285 3002.06 27027
1990 824391 3194.85 27250
1991 815581 3314.434 27086
1992 824769 3561.726 27841
1993 886169 3796.574 27935
1994 1021168 4042.474 28356
1995 1168160 4267.168 28954
1996 1273878 4513.029 29528
1997 1344165 4787.784 30246
1998 1441272 5132.366 31651
1999 1553622 5491.189 32312
2000 1741267 5899.421 33568
2001 1891827 6174.041 34149
2002 1997008 6454.096 34848
2003 2102932 6766.75 35446
2004 2220119 7179.226 36302
2005 2320555 7605.264 36527
2006 2456716 8039.724 37621
2007 2609477 8413.372 38119
2008 2643789 8592.555 38125
2009 2555017 8567.045 37728
2010 2646811 8840.849 38161
2011 2757073 9188.898 38769
2012 2918258 9531.063 39765
2013 3093386 9815.126 38974
2014 3314567 10290.9 40251
2015 3413612 10838.64 41598
2016 3644200 11326.88 42003
2017 3832740 11822.06 42791
Data on real consumption (C), real disposable income (Y), and availability of credit (CR) is provided for U.S.
a. Estimate the longrun consumption model. Consumption model: logC = Intercept + logY + logCR + . is the error term. Report and discuss the long run results of the consumption model.
Explanation / Answer
This consumption model can very well be plotted as a time series model in any of the regression analysis modelling method.
Here the data series can be modelled in any such modelling method and the result can be drawn as under: coding in "R"
# A preliminary logarithmic regression
model_ols <- lm(log(C) ~ log(Y)+log(CR), data=Data)
summary(model_ols)
And the result:
lm(formula = log(C) ~ log(Y) + log(CR), data = Data)
Residuals:
Min 1Q Median 3Q Max
-0.31797 -0.04581 0.00728 0.07279 0.30523
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -16.6883 1.8501 -9.020 2.43e-13 ***
log(Y) 1.9017 0.2783 6.833 2.52e-09 ***
log(CR) 0.3844 0.0738 5.209 1.82e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1331 on 70 degrees of freedom
Multiple R-squared: 0.9928, Adjusted R-squared: 0.9926
F-statistic: 4857 on 2 and 70 DF, p-value: < 2.2e-16
As the Pr(>|t|) value is much lesser than the null hypothesis, the model can well be accepted as a proper one.
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