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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 3-2 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” 7-3 Graphics: productivity, factors of production and output 7-4 How to infer productivity from data on output and factor accumulation Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7-5 A formula to calculate productivity from data on output and factor accumulation 7-6 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 7-7 Table 7.2 Development Accounting Development accounting = application of formula to compute productivity from data on output and factor accumulation 7-8 Figure 7.2 & 7.4 Role of Factors of Production and Productivity in Determining Output per Worker, 2009 7-9 Table 7.3 Data for Calculating Productivity Growth in Erewhon Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7-10 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 Growth accounting – where the formula comes from Start from equation in levels: 7-12 Figure 7.5 & 7.6 Role of factors of production and productivity in determining Gdp growth, 1970–2005 7-13 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 7-14 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? 7-16 Decompose A into T (technology) and E (efficiency) 10-17 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: 7-18 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) 10-19 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 10-20 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 Figure 10.3 Efficient Allocation of Labor Between Sectors 10-22 Figure 10.4 Overallocation of Labor to Sector 1 10-23