Growth and Output Measurement in the World

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1 Carnegie Mellon University Research CMU Society for Economic Measurement Annual Conference 2015 Paris Jul 24th, 2:30 PM - 4:30 PM Capital Input and the Sources of U.S. Economic Growth across Industries: A Comparison of Alternative Approaches Jon D. Samuels U.S. Bureau of Economic Analysis, jon.samuels@bea.gov Jay Stewart Bureau of Labor Statistics, stewart.jay@bls.gov Erich H. Strassner U.S. Bureau of Economic Analysis, erich.strassner@bea.gov David B. Wasshausen U.S. Bureau of Economic Analysis, david.wasshausen@bea.gov Follow this and additional works at: Part of the Economics Commons Jon D. Samuels, Jay Stewart, Erich H. Strassner, and David B. Wasshausen, "Capital Input and the Sources of U.S. Economic Growth across Industries: A Comparison of Alternative Approaches" ( July 24, 2015). Society for Economic Measurement Annual Conference. Paper This Event is brought to you for free and open access by the Conferences and Events at Research CMU. It has been accepted for inclusion in Society for Economic Measurement Annual Conference by an authorized administrator of Research CMU. For more information, please contact research-showcase@andrew.cmu.edu.

2 Capital Services Measurement and the Sources of U.S. Economic Growth Jon Samuels (BEA) Jay Stewart (BLS) Erich Strassner (BEA) Dave Wasshausen (BEA) 24 July 2015 The views expressed in this paper are solely those of the authors and not necessarily those of the U.S. Bureau of Economic Analysis, or the U.S. Bureau of Labor Statistics. 1

3 Introduction Economic modeling is in large part the art of astute simplification. With the goal of drawing general conclusions. Similar for economic statistics. Potential problem: Conclusions may be an artifact of the simplifications. 2

4 Introduction This paper: modeling (measuring) capital services and the sources of U.S. economic growth. Long-standing call for statistics on the sources of growth o Solow (1957), Denison (1967), Griliches and Jorgenson (1967) o Postwar Recovery, Big Slump, IT Boom, the Great Recession o differences between the BEA and BLS estimates have led many researchers to construct their own measures -Jorgenson and Landefeld (2006) in A New Architecture for the U.S. National Accounts 3

5 Introduction Output measurement: SNA, widely applied. Input measurement: SNA, OECD manuals, less widely applied. This has important consequences for analysis. Input measurement: conceptual and implementation issues. This paper: capital services. 4

6 Introduction Compare two approaches: 1) BLS 2) Jorgenson et al. o Major conceptual difference: vintage accounting. o Implementation differences: rates of return, negative services prices, capital gains, taxes. Findings: sources of growth similar, some differences across industries. o Related to implementation, not simplification. 5

7 Capital Services Measurement Three Steps 1) Calculate the productive capital stock o Perpetual Inventory Method (PIM) o Assume constant quality units o Assume a functional form for deterioration (age-efficiency function) o By asset and industry 6

8 Capital Services Measurement General Methodology 2) Calculate the capital service price (rental rate of capital) Opportunity cost concept that accounts for depreciation, forgone returns, taxation, and capital gains o Age-price function o Wealth stock o Internal rate of return o By asset and industry 3) Aggregation the productive stock into estimates of capital service flows using capital service prices as weights. 7

9 The Productive Capital Stock Perpetual Inventory Method The productive capital stock: S K k,i,t = s(a)i k,i,t a a=0 s(a) is the age-efficiency function (a = age) I k,i,t a is investment (asset k, industry i, time t-a) JHS (BEA) geometric: s(a) = (1 δ k ) a 8

10 BLS s Age-Efficiency Function I BLS hyperbolic: s(a, Ω) = (Ω a) (Ω βa) if a < Ω Ω is the maximum service life of the asset β is a shape parameter: If β > 0 s(a, Ω) is concave If β < 0 s(a, Ω) is convex BLS assumes β = 0.5 for equipment and β = 0.75 for structures 9

11 Hyperbolic Age-Efficiency Profiles for Different Ω Ω = 3 Ω = 7 Ω = 11 Ω = 15 Ω = 19 10

12 BLS s Age-Efficiency Function II Note that Ω is the maximum service life of an asset, but we have data on the average service life of assets in a category BLS accounts for heterogeneity of service lives within an asset category through the cohort age-efficiency function: s (a, Ω ) = Ω max Ω min f Ω (a, x) s(a, x)dx f Ω (a, x) is the distribution of service live within an asset category BLS assumes that f Ω (a, x) is a modified truncated normal distribution 11

13 Final Capital Stock Equations JHS (BEA): S K k,i,t S = K k,i,t 1 (1 δ a ) + I k,i,t Geometric Deteriorate rate does not vary with age, so no need to keep track of vintage BLS: S K k,i,t Ω max = s (a, Ω )I k,i,t a a=0 Hyperbolic Deterioration rate varies with age of asset, so it is necessary to keep track of the vintage of investment 12

14 The Age-Price Function and the Wealth Stock The wealth stock is given by: K t W = p(τ t) I 2t τ τ=t where: s(a) = (1 δ k ) a s(a) = s (a, Ω ) = p(a, Ω ) = α=a s(α) (1 r)α a s(α) (1 r) α Ω max Ω min α=0 f Ω (a, x) s(a, x)dx JHS (BEA) BLS 13

15 Example Photocopy and Related Equipment BEA: Depreciation rate = 18 percent per year Average service life = 9 years BLS: Average service life = 11 years How much difference does it make? 14

16 Age-Efficiency and Age-Price Profiles 1 Age-Efficiency/Price Functions Age-Efficiency L-bar = 11 Age-Price L-bar = 11 Geometric Age-Efficiency/Price 15

17 Simulated Capital Stock Alternative Capital Stock Measures BLS K Stock L-bar=9 (BEA SL) BLS K Stock L-bar=11 (BLS SL) K Stock geometric - BEA 16

18 Growth Rates 0.05 Log Change in Alternative Capital Stock Measures Growth in ln(kstock9) Growth in ln(kstock11) Growth in ln(dkstock_geo) 17

19 Rental Prices I The rental price formula is essentially the same the BLS and JHS methodologies The rental price formula accounts for: The (internal) rate of return Changes in the price of new assets Economic depreciation Taxes 18

20 Rental Prices II Most of the differences are due to differences in implementation Treatment of negative rental prices Calculation of capital income (mainly calculation of noncorporate capital income) Treatment of land input We are still investigating differences in implementation 19

21 Empirical Exercise Impact of BLS assumptions versus Jorgenson et al. (JHS) assumptions on estimates of U.S. sources of growth. Industry-level production account. o Rosenthal, Russell, Samuels, Strassner, Usher (2014). o Forthcoming Growth and Stagnation in the World Economy ed. by Jorgenson, Fukao, Timmer Growth accounting: bottom up from industry to aggregate. o Direct aggregation across industries. 20

22 Empirical Exercise Growth accounting details: o Industry MFP growth: ln MFP ln Q w ln Q w ln Q w ln Q Useful definition: ln Q ln Q ln Q Aggregation: j j Kj Kj Lj Lj Xj Xj QKj Kj Zj ln MFP ln Q w ( ln Q ln Q ) w ln Q w lnq j j Kj QKj Zj Lj Lj Xj Xj w K, j L, j ln V wj ( ln QQKj ln QZj ) wj ln QLj wj ln MFPj j wv, j wv, j wv, j w 1 21

23 Productive Stock Growth : JHS versus BLS Data processing, internet publishing, and other information services Amusements, gambling, and recreation industries Support activities for mining Forestry, fishing, and related 0.0 activities

24 Capital Input Growth : JHS versus BLS Securities, commodity contracts, and investments Educational services Computer systems design and related services Management of companies and enterprises Other services, except government Air transportation 23

25 Capital Quality Growth : JHS versus BLS Educational services Securities, commodity contracts, and investments Management of companies and enterprises Other services, except government 24

26 Capital Contributions to Industry Output Growth Pipeline transportation Transit and ground transportation Management of companies

27 Industry MFP Contributions to Agg. VA Growth Real Estate

28 Sources of Aggregate Growth less Contributions BLS Value-Added Capital Input Labor Input College Labor Non-college Labor MFP Contributions JHS Value-Added Capital Input Labor Input College Labor Non-college Labor MFP Notes: Average annual percentages. Aggregate value added growth is the aggregate of share weighed industry value added growth. The contribution of capital, labor, and TFP is the domar-weighted industry contributions. 27

29 Quality Growth Differences and Industry Characteristics 28

30 Conclusions Aggregate estimates of the sources of growth largely unaffected between these two measures. o Some differences across industries. o Probably related to implementation. Puzzles remain, e.g.: o Investment over the business cycle. o Rates of return across industries. o Utilization. o Land quality. Shouldn t trivialize capital measurement. 29

A Prototype BEA/BLS Industry Level Production Account for the United States

A Prototype BEA/BLS Industry Level Production Account for the United States Susan Fleck* Steven Rosenthal* Matthew Russell** Erich H. Strassner** Lisa Usher* Final version: November, 2012 Presented at