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 3-2

Where k α h 1-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 = AK α (hL) 1-α, we can rewrite in per-worker terms and obtain y=Ak α h 1-α. In turn:

7-4 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

7-6 A formula to calculate productivity from data on output and factor accumulation

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

Development accounting = application of formula to compute productivity from data on output and factor accumulation 7-8 Table 7.2 Development Accounting

7-9 Figure 7.2 & 7.4 Role of Factors of Production and Productivity in Determining Output per Worker, 2009

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=Ak α h 1-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 g y = g A + (α g k + (1-α) g h ) and then used to compute the growth rate of productivity as a residual: g A = g y - (α g k + (1-α) g h ) Not by chance g A is labelled the “Solow residual” 7-11

Growth accounting – where the formula comes from 7-12 Start from equation in levels:

7-13 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 g A has also been named the “summary of our ignorance”. The same applies to our measure of “A” (g A 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 g A 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 g A is not (check!) So if, due to imperfect measurement, actual measures of A are biased, measures of g A need not be biased 7-14

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? 7-16

10-17 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 If this only came from technology, this means that E in the US economy remained constant Then T 2005,US = T 1970,US (1.0066) 35 More generally, for a technology developed G years ago: T 2005,US = T 2005-G,US (1+g) G Now: suppose that India is G years backwards in terms of technology than the US. It follows that: T 2005,US = T 2005,India (1.0066) 35 And then: 7-18

Had efficiency stayed constant, then the technology gap between the US would be 0.94 (= ) Technology gap between India and the US

Conclusion: most of the productivity gap between India and the US would stem from efficiency In turn, the efficiency gap would be =0.37 (so as to give A India /A US =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 7-21

10-22 Figure 10.3 Efficient Allocation of Labor Between Sectors

10-23 Figure 10.4 Overallocation of Labor to Sector 1