# 08 Productivity

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productivity

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Chapter 7MEASURING PRODUCTIVITY

ProductivityProductivity = 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 productivity3-2

Productivity in the Cobb-Douglas production functionStarting from Y = AK(hL)1-, we can rewrite in per-worker terms and obtain y=Akh1-. In turn:

Where kh1- represents an aggregate measure of factors of production (per worker) and A is productivity7-3

Graphics: productivity, factors of production and output

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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 =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, 2005

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Table 7.3 Data for Calculating Productivity Growth in Erewhon

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Growth accountingGrowth accounting is a technique to compute productivity growth (from Solow 1957) The same formula y=Akh1- 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 + ( gk + (1-) gh) and then used to compute the growth rate of productivity as a residual: gA = gy - ( gk + (1-) gh) Not by chance gA is labelled the Solow residual7-11

Figure 7.5 & 7.6 Role of factors of production and productivity in determining Gdp growth, 19702005

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The summary of our ignoranceThe 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

Chapter 10EFFICIENCY

Why productivity differences over time and across countriesProductivity 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

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

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How to go from A to T and EStarting 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)35And then:7-17

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)10-18

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 efficiency10-19

Five types of inefficiencyInefficiency 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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