Question

Nominal Gross Domestic Product and Personal Consumption Expenditure in $billions 1929-2016
Source: Federal Reserve Bank of St. Louis
Year	Personal Consumption Expenditure	Nominal GDP
1929-01-01	77.4	104.6
1930-01-01	70.1	92.2
1931-01-01	60.7	77.4
1932-01-01	48.7	59.5
1933-01-01	45.9	57.2
1934-01-01	51.5	66.8
1935-01-01	55.9	74.3
1936-01-01	62.2	84.9
1937-01-01	66.8	93.0
1938-01-01	64.3	87.4
1939-01-01	67.2	93.5
1940-01-01	71.3	102.9
1941-01-01	81.1	129.4
1942-01-01	89.0	166.0
1943-01-01	99.9	203.1
1944-01-01	108.6	224.6
1945-01-01	120.0	228.2
1946-01-01	144.3	227.8
1947-01-01	162.0	249.9
1948-01-01	175.0	274.8
1949-01-01	178.5	272.8
1950-01-01	192.2	300.2
1951-01-01	208.5	347.3
1952-01-01	219.5	367.7
1953-01-01	233.0	389.7
1954-01-01	239.9	391.1
1955-01-01	258.7	426.2
1956-01-01	271.6	450.1
1957-01-01	286.7	474.9
1958-01-01	296.0	482.0
1959-01-01	317.5	522.5
1960-01-01	331.6	543.3
1961-01-01	342.0	563.3
1962-01-01	363.1	605.1
1963-01-01	382.5	638.6
1964-01-01	411.2	685.8
1965-01-01	443.6	743.7
1966-01-01	480.6	815.0
1967-01-01	507.4	861.7
1968-01-01	557.4	942.5
1969-01-01	604.5	1019.9
1970-01-01	647.7	1075.9
1971-01-01	701.0	1167.8
1972-01-01	769.4	1282.4
1973-01-01	851.1	1428.5
1974-01-01	932.0	1548.8
1975-01-01	1032.8	1688.9
1976-01-01	1150.2	1877.6
1977-01-01	1276.7	2086.0
1978-01-01	1426.2	2356.6
1979-01-01	1589.5	2632.1
1980-01-01	1754.6	2862.5
1981-01-01	1937.5	3211.0
1982-01-01	2073.9	3345.0
1983-01-01	2286.5	3638.1
1984-01-01	2498.2	4040.7
1985-01-01	2722.7	4346.7
1986-01-01	2898.4	4590.2
1987-01-01	3092.1	4870.2
1988-01-01	3346.9	5252.6
1989-01-01	3592.8	5657.7
1990-01-01	3825.6	5979.6
1991-01-01	3960.2	6174.0
1992-01-01	4215.7	6539.3
1993-01-01	4471.0	6878.7
1994-01-01	4741.0	7308.8
1995-01-01	4984.2	7664.1
1996-01-01	5268.1	8100.2
1997-01-01	5560.7	8608.5
1998-01-01	5903.0	9089.2
1999-01-01	6307.0	9660.6
2000-01-01	6792.4	10284.8
2001-01-01	7103.1	10621.8
2002-01-01	7384.1	10977.5
2003-01-01	7765.5	11510.7
2004-01-01	8260.0	12274.9
2005-01-01	8794.1	13093.7
2006-01-01	9304.0	13855.9
2007-01-01	9750.5	14477.6
2008-01-01	10013.6	14718.6
2009-01-01	9847.0	14418.7
2010-01-01	10202.2	14964.4
2011-01-01	10689.3	15517.9
2012-01-01	11050.6	16155.3
2013-01-01	11361.2	16691.5
2014-01-01	11863.4	17393.1
2015-01-01	12283.7	18036.6
2016-01-01	12757.9	18569.1

Regress Consumption against the GDP from the data sheet. Include the Excel ANOVA table.Although irrelevant run a "F" test as well as individual coefficient test . Write a short paragraph discussing the results. For example, how this information can be used to forecast future consumption or any other interesting conclusions you can draw Material in your textbook as well as outside reading can be very helpful

Answer 1

Below are regression results:

Dependent variable: Personal consumption	Coefficients	Standard Error	t Stat	P-value
Intercept	-82.7454	13.8165	-5.9889	0.0000
Nominal GDP	0.6797	0.0020	348.2969	0.0000

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1226757365.46	1226757365.46	121310.74	3.134077770323E-137
Residual	86	869676.76	10112.52
Total	87	1227627042.22

Regression Statistics
Multiple R	0.999645727
R Square	0.999291579
Adjusted R Square	0.999283342
Standard Error	100.5610286
Observations	88

The nominal GDP is positively associated with Personal consumption. This is indicated by the positive coefficient which 0.67 and is also statistically significant at even 1% level. It indicates that $1 change in nominal GDP results in $0.67 change in personal consumption.

The result of t-test of the coefficient of Nominal GDP is statistically significant since the p-value is close to 0.

The p-value of F test (in ANOVA model) is also close to zero which implies that the current model indeed has a good fit.

This sign of slope coefficient is consistent with what we have read in macroeconomic theory. That is, as income increases, the consumption changes by a positive quantity times the change in income. In a way, 0.67 can be seen as a marginal propensity to consume.

The intercept coefficient is however negative which is inconsistent with theory. This doesn't make sense. At zero nominal GDP/income, the consumer will still consume something. However, the regression results suggest that the consumer instead saves at zero income.