Term Project

An exercise in macroeconomics:

Recall that in ECO 1002 or any other intro macro, total consumption expenditure is a function of disposable income (or after-tax income).  Specifically, we have:

Consumption  =  a constant  +  (marginal propensity to consume) * (disposable income),   

and 'marginal propensity to consume' is a fixed unknown number.  The constant term in the above equation is often assumed to be zero but here, we take a more general assumption that the constant can be any number but the number is unknown to us.  Note that the above equation as taught in econ theory has no random term in it.

The following (ancient) data (sample) is obtained from a government publication, Economic Report of the President:

Year                        Disposable Income                   Consumption

1970                        751.6                                           672.1

1971                        779.2                                            696.8

1972                        810.3                                            737.1

1973                        864.7                                            767.9

1974                        857.5                                             762.8

1975                        874.9                                             779.4

1976                        906.8                                             823.1

1977                        942.9                                             864.3

1978                        988.8                                             903.2

1979                       1015.7                                            927.6

The above numbers are in billions of 1972 dollars, i.e., they are adjusted for inflation (or computed using 1972 prices) which means they are real GDP and real consumption.

Suppose we are interested in the value of the marginal propensity to consume in the above consumption function.   Please estimate its value with the above data and describe your model, estimation procedure and result in a written report to me (due on the final exam day).   Your report should include the following:

(a) Specify the statistical model that you are going to use.  If it is a linear model, which variable (consumption or income) is the dependent variable and which is the independent variable?  Which quantity/notation in the model is the marginal propensity to consume?

(b) Find the estimate for the marginal propensity to consume by running a regression in Excel (or other software of your choice).  You must submit your regression output/printout from Excel (or another program that you choose).

(c) Is the estimate in part (b) the (true) value of the marginal propensity to consume?  Explain.  Is the estimate in part (b) close to the true value of the marginal propensity to consume?  Explain.  Also, can you tell from your estimate, what is the true value of the marginal propensity to consume?

(d) Verify that your estimate in part (b) is correct by manually computing the least squares estimate for the marginal propensity to consume.  You must submit a table (similar to the one that we did in class) that shows your calculation. 

(e) According to your estimate/answer in part (b), if income increases by 1, what is your estimate of the change in consumption? What is the change if income increases by 2?