# The Growth Facts Exercise

Edward C. Prescott

The objective of this assignment is to compute the averages of the following statistics for the post Korean War U.S. economy (1954 -1996, quarterly data):

(i) The growth rate of per capita real output;
(ii) The growth rate of the population;
(iii) The fraction of total income that is paid to owners of capital;
(iv) The fraction of total income that is paid to suppliers of labor service;
(v) The investment to output ratio;
(vi) The capital to output ratio.

There are two important issues that must be addressed.  First, we need an accounting system in which inputs and outputs are consistent with each other.  Second, we need to check that the averages we compute are meaningful in that there are no significant trends in the numbers we are averaging.  Here are some steps to follow:

2. Compute capital's claim against product,  RKt . This capital stock does not include the stock of consumer durables.

3. Using RKt and the depreciation DKt on this capital stock, compute the average return on this capital it-1 .

4. Using these it-1 , the stocks of consumer durables KCD,t  and the depreciation DCD,t , compute rental prices rCD,t  for consumer durables.

5. Compute C, X (investment), R, W, and Y, where C includes the services of consumer durables and R includes rental income that owners of consumer durables earn by renting their consumer durables to themselves.

6. Compute the data series (i)-(vi).

Hand in the following: (NOTE: Report quarterly values unless otherwise specified.)

1. Formula for your estimate of K's share of GNP. This is the K in the data set.

2.

3. Formulae for the quarterly rental income and the quarterly rental rate of the K in the data set.

4.

5. Formula for the quarterly i(t-1) . The formula should involve date t variables only.

6.

7. Formula for the quarterly rental price of consumer durables.

8.

9. Formulae for quarterly C and X in the theory.

10.

11. Formulae for quarterly W and R in the theory.

12.

13. Report average quarterly and annual growth rates of  income per working-age person and working-age population. The date t growth rate of a variable, say variable z, is [z(t)-z(t-1)] / z(t-1) .

14.

15. Report quarterly averages of X/Y, W/Y and K/Y. Here, Y is at a quarterly rate.

16.

17. Hand in plots of W/Y, C/Y, K/Y and hours per person versus time (quarters). There should be one variable per plot.

WARNING:
The flow variables are quarterly numbers at annualized rates. This implies that if GNP is \$100 in 1960.2 then the value of all final goods produced in the second quarter of 1960 was \$25.