1. Total Factor Productivity
Analytical Exercises

2. Simple vs. Compound Interest Rate
If you have a time deposit and receive a simple interest rate, then, after 1 year, your account will increase by the interest rate.
If you receive a compound interest rate, rr(n), you may receive your extra income in increments which appear n times per year.

3. Define the compound interest rate with continuous compounding ρ = rr(n→∞), we calculate growth with the anti-log, e,
Refer to the log-difference as the continuous growth rate,

4. Natural Logarithmic Function
Natural Log Function has a number of useful (for the study of productivity) properties
Log of a Product is the sum of the logs
Log of exponent
Derivative of logarithm is the inverse

5. Growth Accounting
To study growth, take derivative of production function with respect to time. By the chain rule,
Notation for
CRTS implies βt = 1-αt, Price taking implies 1-αt is labor’s share of income.

6. Continuous Rate of Change
The time derivative of the logarithm of time dependent variable is the variables’ continuous rate of change.
Most economic series are observed only intermittently. We approximate the continuous rate of change with the first difference of the natural log:

7. Cobb-Douglas Cobb-Douglas function is log-linear
Easy to do Growth Accounting because factor intensities are constant. TFP growth is proportional to technology growth.

8. TFP Growth
TFP is log linear

9. TFP growth rate is the gap between GDP growth rate and the weighted average of the growth rate of the factors of production.

10. Total Factor Productivity
Total factor productivity measures the total effectiveness of an economy in applying all of its factors of production.
TFP is a geometrically weighted average of capital and labor productivity with factor intensity, at and 1-at = used as weights.

11. Cobb-Douglas TFP Since we can write
Under Cobb-Douglas, the level of TFP is a geometrically weighted function of capital productivity and labor productivity.

12. Growth Accounting Exercise: Celtic Tiger
Economy of Ireland has been one of the most successful in Europe in recent years transforming from one of the poorer countries of Europe to one of the richest over a period of about 25 years.
Growth accounting is a technique that economists use as a first step in explaining the sources of growth.

13. Growth Accounting
The growth accounting equation divides the sources of growth into 3 parts
Growth due to labor (i.e. growth in labor weighted by labor intensity, βt)
Growth due to capital (i.e. growth in capital weighted by capital intensity, αt)
Total Factor Productivity Growth (i.e. change in the production function itself).

14. Economic Growth Rates

15. Data
Question: What part of Irish growth is derived from labor growth, capital growth, or TFP growth?
Irish data is from " Marcel P. Timmer, Gerard Ypma and Bart van Ark (2003), IT in the European Union: Driving Productivity Divergence?, GGDC Research Memorandum GD-67 (October 2003), University of Groningen, Appendix Tables

16. Use approximation of growth accounting function
For every year, assume CRTS and write the approximate equation
Approximate labor intensity with the average of labor share of income in the previous year and the current year.

17. Irish Data

18. Growth Accounting

19. Contribution to Growth

20. Growth Accounting Results
Growth Accounting suggests that approximately 30% of the growth in Irish GDP is due to growth in the capital stock about 10% is due to growth in the labor input and about 60% is due to TFP growth.
Of course, this brings up the question, why did TFP grow so much.
Note, we also did not adjust labor for quality improvements.

21. Cobb-Douglass
Easier to calculate if we assume constant TFP growth. Previous slide shows average (1-α) ≈2/3. Assume Cobb-Douglas production function and use this value.
Note average of ΔlnX from period 1 to T is
So we only need to know start and stop values to calculate Growth Accounting. Results, not much different.

22. Average TFP Growth Cobb DouglasQ K L
1980
32,509
55,335
2,230
2001
116,729
149,178
2,903
Average Continuous Growth Rate
1-α = 2/3
ΔlnQ
ΔlnK
ΔlnL
0.053
0.041
0.011
αΔlnK
(1-α)ΔlnL
ΔlnTFP
0.014
0.007
0.032

23. Item for Discussion East Asian Miracle
Another set of miracle economies over the last 30 years have been the economies of East and Southeast Asia.
What is the source of growth in these economies?
What are the implications for future growth.