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Chapter 7
MEASURING
PRODUCTIVITY
Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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
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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:
Where kαh1-α represents an aggregate measure of “factors of
production” (per worker) and A is “productivity”
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Graphics: productivity, factors of
production and output
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How to infer productivity from data on
output and factor accumulation
Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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A formula to calculate productivity from
data on output and factor accumulation
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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
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Table 7.2 Development Accounting
Development accounting = application of formula to compute
productivity from data on output and factor accumulation
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Figure 7.2 & 7.4 Role of Factors of Production
and Productivity in Determining Output per
Worker, 2009
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Table 7.3 Data for Calculating
Productivity Growth in Erewhon
Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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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”
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Growth accounting – where the
formula comes from
Start from equation in levels:
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Figure 7.5 & 7.6 Role of factors of production
and productivity in determining Gdp growth,
1970–2005
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The “summary of our ignorance”
The Solow residual gA has also been named the “summary of our ignorance”. The
same applies to our measure of “A” (gA is growth of A)
Why a measure of ignorance?
Simple: if we measure imperfectly y, k or h, any mis-measurement 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.
Implication: We should be careful interpreting their values
Quick quiz: 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!)
• So if, due to imperfect measurement, actual measures of A are biased, measures
of gA need not be biased
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Chapter 10
EFFICIENCY
Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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?
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Decompose A into T (technology)
and E (efficiency)
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How to go from A to T and E
Starting point: the US growth of A was 0.66% per year in 19702005. If this only came from technology, this means that E in
the US economy remained constant
Then
T2005,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:
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Technology gap between India and the US
Had efficiency stayed constant, then the technology gap
between the US would be 0.94 (=1.0066-10)
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In turn, the efficiency gap would be
=0.37 (so as to give AIndia/AUS=0.35)
Conclusion: most of the productivity gap between India and the US
would stem from efficiency
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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
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Figure 10.3 Efficient Allocation of
Labor Between Sectors
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Figure 10.4 Overallocation of
Labor to Sector 1
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