Econ. 153a Fall 1996 C. Sims

## Growth Accounting Exercise

Right click on the file pwt56.wks (For Penn World Tables, version 5.6) and choose the "Save As" option to obtain your copy of a file of time series from 1965 through 1990 for Taiwan, Korea, and the US on capital per worker (KAPW) and GDP per worker (RGDPW). They are in an old Lotus spreadsheet format that any spreadsheet program should be able to read.

Under the assumption of a Cobb-Douglas production function

,

the growth accounting formula can be written in terms of output per worker and capital per worker as

.

Using this formula, approximating the time derivatives with annual changes (so

,

for example), construct a measure of the "contribution to productivity growth of capital deepening." You will need to assume something about . Because the best measure of it is uncertain, it is common practice (as in the Bosworth and Collins paper) to assume it to be constant, but to try a few different values. You should try setting it to .20, .30, and .45, which covers the range of what most economists would think to be reasonable guesses.

For each country make a plot of the actual time path of RGDPW together with the time paths of your estimates of the contribution of capital deepening. Answer the following questions about the results.

1. Do you reproduce the finding of Bosworth and Collins and of Alwyn Young before them that the Asian countries' growth is largely explained by the capital-deepening term?
2. Can you see a slowdown in the contribution of capital-deepening in the US that would match the hypothesis that the wage slowdown, starting in the mid-70's, is due to a slowdown in capital accumulation?
3. What are the biggest differences between the simple exercise we are conducting here and what Bosworth and Collins did? Given these differences, are the differences in results surprisingly big? Surprisingly small?

You can submit your answer to the exercise as an email attachment, if you like. Probably the simplest way would be to do the calculations and plots within a spreadsheet, and then write answers to the discussion questions in an editor or word processor. I will be able to read files written by Excel, MS Word, WordPerfect, Quattro Pro, or Lotus, as well as ordinary text files and postscript files. There might be some problem with files produced by the very latest versions of programs other than Excel or MS Word, but I'll let you know if there are difficulties. If you have difficulties with sending such files, you can hand in the exercise answers on paper in class.

The due date is Wednesday, September 18. I hope to be able to discuss the exercise in class that day. If it turns out that a lot of people get stuck on the mechanics of doing this, the due date will be extended.