Chicken Consumption - Statistic

Introduction:   The subject of this assignment is to estimate the consumption function in the United States.  Consumption fn data, which posted on Campus Web, will be used to estimate both short run and long run consumption function in the U.S.  This data contains Real Personal Consumption Expenditures and Real Disposable Personal Income data from 1947-01-01 to 2012-01-01 and 1959-01-01 to 2012-05-01 retrospectively.  In order to estimate the consumption function, Keynesian consumption function is in use, which expresses consumption as a function of disposable income.  Specifically, it states as ,  where   represents the aggregate personal consumer expenditures (PCE) in year t, and  represents the disposable income in year t.    is called the marginal propensity to consumer (MPC).  Economists have found that the value of MPC differs in the short run and the long run.  In this case, Excel is used to run the simple linear regress to demonstrate the relationship between personal consumer expenditures and disposable income. [pic 1][pic 2][pic 3][pic 4]

To better estimate the consumption function and its correlation between disposable income and personal consumer expenditure, a scatter plot is useful.

[pic 5]

Where           SER = 130.81[pic 6][pic 7]

                (0.0015)

        T-Stat    623.17

             N=213 (Date from 1959 to 2012)

[pic 8]

Where              SER=30.80[pic 9][pic 10]

                (14.52)       (0.0045)

        T Stat       5.10        190.91

        N = 84 (Date from 1960 to 1980)

Comparing short run and long run equation, it is easy to find out that there is no intercept in long run, whereas the intercept for short run is 74.11. This means that in the long run, if there is no disposable income, there would be no expenditures.   For every dollar of disposable income increase, the personal consumer expenditure will increase by 0.92 dollar.  However, in short run, even there is no disposable income in a given year, the personal consumer expenditure would be 74.11.  This is called autonomous consumption.  It represents that the minimum level of consumption needed for any person in order to survive.  For every dollar of disposable income increase in short run, it will increase the personal consumer expenditure by 0.86 dollar.

When the disposable income in a year reach $1,235.17, the long run and short run personal consumer expenditure would breakeven.  As the disposable income increase over $1,235.17, it demonstrated that there would be more expenditure in long run than short run.

To best estimate the correlation between disposable income and personal consumer expenditure, a residual plot will use to determine if the linear regression model is appropriate for the data or not.

[pic 11] [pic 12]

For both long run and short run, the points are randomly dispersed around the horizontal axis, which means it is appropriate to use a linear regression model as the methology to estimate the consumption functions.