For the period 1970-1991 for the United States the following two rival consumption models were estimated using the data on personal consumption expenditure (PPCE) and per capita disposable personal income (PDPI). Model A: PPCE, = 1299,05+0,9204PDPI,+ 0,0931PDPI_1 R = 0,988 t= (4,03) (6,01) (0,63) AIC = 12,91 SC=13,06 Model B: PPCE, =-841,85+0,7117PDPI,+0,2954PPCE, R = 0,9912 t= (-2,41) (5,46) (2,36) AIC=12,66 SC=12,81 To choose between those two alternative models Davidson Mackinnon J test is applied. The results are as follows: PPCE, = -1322,79+0,7061PDPI, - 0,4357PDPI,+2,1335PPCE R =0,9932 SE = (832,15) (0,5058) (0,1987) (0,6437) where PPCE are the estimated PPCE values from Model B. PPCE, = -6549,86+5,1176PDPI, + 0, 6302PPCE,1- 4, 6776PPCE R = 0,9920 SE = (2622,46) (2,0129) (0,1845) (17,4082) where PPCE are the estimated PPCE values from Model A. a) Decide the better model by using model selection criteria of Akaike and Schwarz. b) According to the J test results which model is better?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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The model with the lowest AIC value being considered the ‘best’.
From the provided information, the AIC value of Model A is 12.91, and the AIC model of Model B is 12.66.
Therefore, Model B is a better model than model A because Model B having the lowest AIC value.
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