08 Productivity
-
Upload
froso-erotokritou -
Category
Documents
-
view
16 -
download
1
description
Transcript of 08 Productivity
![Page 1: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/1.jpg)
Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Chapter 7
MEASURING PRODUCTIVITY
![Page 2: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/2.jpg)
Productivity
Productivity = effectiveness with which factors of production (such as K, L) are converted into output
So far: looked at accumulation of factors of production DISREGARDING productivity differences
• “A” often assumed to be the same across countries
This is typically not the case
We use “development accounting” and “growth accounting” to learn about and quantify the role of productivity
3-2
![Page 3: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/3.jpg)
Where kαh1-α represents an aggregate measure of “factors of production” (per worker) and A is “productivity”
7-3
Productivity in the Cobb-Douglas production function
Starting from Y = AKα(hL)1-α, we can rewrite in per-worker terms and obtain y=Akαh1-α.
In turn:
![Page 4: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/4.jpg)
7-4
Graphics: productivity, factors of production and output
![Page 5: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/5.jpg)
Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7-5
How to infer productivity from data on output and factor accumulation
![Page 6: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/6.jpg)
7-6
A formula to calculate productivity from data on output and factor accumulation
![Page 7: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/7.jpg)
7-7
Example: calculating productivity in Country 1 and Country 2
If α=1/3, productivity in country 1 is twice as much as in country 2
![Page 8: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/8.jpg)
Development accounting = application of formula to compute productivity from data on output and factor accumulation 7-8
Table 7.2 Development Accounting
![Page 9: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/9.jpg)
7-9
Figure 7.2 & 7.4 Role of Factors of Production and Productivity in Determining Output per Worker, 2005
![Page 10: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/10.jpg)
Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7-10
Table 7.3 Data for Calculating Productivity Growth in Erewhon
![Page 11: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/11.jpg)
Growth accounting
Growth accounting is a technique to compute productivity growth (from Solow 1957)
The same formula y=Akαh1-α that we used before can be transformed in growth rates (How? Take the derivative of both left-hand and right-hand side of the equation with respect to time and then divide the result by y)
The following expression is obtained
gy = gA + (α gk + (1-α) gh)
and then used to compute the growth rate of productivity as a residual:
gA = gy - (α gk + (1-α) gh)
Not by chance gA is labelled the “Solow residual”
7-11
![Page 12: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/12.jpg)
7-12
Figure 7.5 & 7.6 Role of factors of production and productivity in determining Gdp growth, 1970–2005
![Page 13: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/13.jpg)
The “summary of our ignorance”
The Solow residual gA has also been named the “summary of our ignorance”. But the same applies to our measure of “A”
Why? For a simple reason
If we measure imperfectly y, k or h, any mismeasurement will affect the measured value of gA and A
So our measures of productivity levels and growth are a mixture of actual productivity and measurement error. We should be careful interpreting their values
More problematic interpreting levels than growth rates• If measured A = z (constant coefficient, different from one) times A (the
true value of A!), this means that our measure of A is biased. But our measure of gA is not (check!)
7-13
![Page 14: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/14.jpg)
Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Chapter 10
EFFICIENCY
![Page 15: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/15.jpg)
Why productivity differences – over time and across countries
Productivity differs a lot between countries. But not all differences are due to technology
This may be true for a country over time
Yet if we compare productivity growth across countries, differences are likely due to something else
• Cellular phones employed everywhere, not just in the US, Finland or Japan
• If people in India use the same tech as in the US, why are their productivity levels 65% lower than the US levels?
EFFICIENCY must play a role
How do we know whether it is technology or efficiency?7-15
![Page 16: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/16.jpg)
10-16
Decompose A into T (technology) and E (efficiency)
![Page 17: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/17.jpg)
How to go from A to T and E
Starting point: the US growth of A was 0.66% per year in 1970-2005. If this only came from technology, this means that E in the US economy remained constant
ThenT2005,US = T1970,US (1.0066)35
More generally, for a technology developed G years ago:T2005,US = T2005-G,US (1+g)G
Now: suppose that India is G years backwards in terms of technology than the US. It follows that:
T2005,US = T2005,India (1.0066)35
And then:
7-17
![Page 18: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/18.jpg)
Had efficiency stayed constant, then the technology gap between the US would be 0.94 (=1.0066-10)
10-18
Technology gap between India and the US
![Page 19: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/19.jpg)
Conclusion: most of the productivity gap between India and the US would stem from efficiency
10-19
In turn, the efficiency gap would be =0.37 (so as to give AIndia/AUS=0.35)
![Page 20: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/20.jpg)
Five types of inefficiency
Inefficiency may stem from five sources• Unproductive activities• Idle resources• Misallocation of factors among sectors• Misallocation of factors among firms• Technology blocking
7-20
![Page 21: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/21.jpg)
10-21
Figure 10.3 Efficient Allocation of Labor Between Sectors
![Page 22: 08 Productivity](https://reader033.fdocuments.net/reader033/viewer/2022061116/54656698b4af9f493f8b4f1a/html5/thumbnails/22.jpg)
10-22
Figure 10.4 Overallocation of Labor to Sector 1