Total Factor Productivity

1 / 23

# Total Factor Productivity - PowerPoint PPT Presentation

Total Factor Productivity . Analytical Exercises. 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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## Total Factor Productivity

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Total Factor Productivity

Analytical Exercises

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.
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,
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
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.

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:
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.
TFP Growth
• TFP is log linear
TFP growth rate is the gap between GDP growth rate and the weighted average of the growth rate of the factors of production.
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.
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.
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.
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).
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
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.
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.
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.

Item for DiscussionEast 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.