08 Productivity

Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Chapter 7

MEASURING PRODUCTIVITY

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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Where kαh1-α represents an aggregate measure of “factors of production” (per worker) and A is “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:

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Graphics: productivity, factors of production and output

Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7-5

How to infer productivity from data on output and factor accumulation

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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

Development accounting = application of formula to compute productivity from data on output and factor accumulation 7-8

Table 7.2 Development Accounting

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Figure 7.2 & 7.4 Role of Factors of Production and Productivity in Determining Output per Worker, 2005

Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7-10

Table 7.3 Data for Calculating Productivity Growth in Erewhon

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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Figure 7.5 & 7.6 Role of factors of production and productivity in determining Gdp growth, 1970–2005

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!)

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Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Chapter 10

EFFICIENCY

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

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Decompose A into T (technology) and E (efficiency)

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:

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Had efficiency stayed constant, then the technology gap between the US would be 0.94 (=1.0066-10)

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Technology gap between India and the US

Conclusion: most of the productivity gap between India and the US would stem from efficiency

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In turn, the efficiency gap would be =0.37 (so as to give AIndia/AUS=0.35)

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