Structural Change in Investment and Consumption: A Unified Approach

Transcription

1 Structural Change in Investment and Consumption: A Unified Approach Berthold Herrendorf (Arizona State University) Richard Rogerson (Princeton University and NBER) Ákos Valentinyi (University of Manchester, CERS HAS, and CEPR) April 27, 2018 Herrendorf, Rogerson, Valentinyi

2 Motivation Structural Change As economies grow, production is reallocated across broad sectors A large literature shows this reallocation importantly affects aggregate outcomes. The literature typically assumes all of investment is produced in manufacturing The sectoral composition of investment is then fixed by assumption. This is convenient and greatly simplifies the analysis, but raises an obvious question: Is abstracting from structural change within investment plausible and innocuous? Herrendorf, Rogerson, Valentinyi 1

3 Our Contribution is to Show that the Answer is No We provide evidence of structural change in investment for the postwar US The share of services value added in investment expenditure has been increasing. As a result, it now exceeds that of goods value added. We model structural change in investment and consumption in a unified way, and show that this leads to three novel insights 1. Technological change becomes endogenously investment specific. 2. BG with SC requires non constant TFP growth in at least one sector. 3. The sector with the lowest TFP growth takes over the economy asymptotically. Herrendorf, Rogerson, Valentinyi 2

4 A Primer on Basic Concepts Industries: collections of establishments that produce similar goods or services. Establishments produce (gross) output from capital, labor and intermediate goods. Establishments sell output to final uses, other establishments, or themselves. Value added: value of output minus value of intermediate goods. Sectors: aggregates of industries with similar characteristics. We focus on goods sector (tangible output) and services sector (intangible output). Final expenditures: value of output delivered to final uses. We focus on investment and consumption. Each is a composite of value added from the goods sector and the services sector. Total requirement matrix gives this decomposition (like in our AER 2013 paper). Herrendorf, Rogerson, Valentinyi 3

5 Evidence Data for postwar US WORLD KLEMS: industry value added, capital and labor services. BEA: annual input-output tables. Method from Herrendorf, Rogerson, Valentinyi (AER, 2013) Decompose final expenditure on investment/consumption into industry value added. Define investment as private/gov t investment and consumption as the rest. Aggregate industries to goods and services sectors (tangible vs. intangible output). Focus on expenditure shares (employment shares show similar patterns). Garcia-Santana, Pijoan-Mas, Villacorta (2016) Document similar facts for 40 countries, plotting country sectoral shares against GDP. Herrendorf, Rogerson, Valentinyi 4

6 Sectoral Composition of Final Investment and Consumption Expenditure (in current dollars) 0.9 Final investment expenditure 0.9 Final consumption expenditure Services value added share Goods value added share Services value added share Goods value added share Herrendorf, Rogerson, Valentinyi 5

7 Disaggregate Subsector Shares in Investment and Consumption 0.6 Investment value added 0.6 Consumption value added Durable Goods Nondurable Goods Durable Goods Nondurable Goods Trade, transport, information Finance, insurance, real estate, business servi Trade, transport, information Finance, insurance, real estate, business servi Health, education, government, art, recreation Health, education, government, art, recreation Stylized Facts about Expenditure Shares (a) Durable Goods and Construction much larger share in investment, decrease in both sectors. (b) Nondurable Goods somewhat larger share in consumption, decrease there. (c) Health, Education larger share in consumption, increase there. Note: (a) and (c) account for most of the higher goods share in investment. (d) FIRE, Business Services similar shares in both sectors, strongly increase. (e) Trade, Transport similar shares in both sectors, decrease somewhat. Herrendorf, Rogerson, Valentinyi 6

8 Relative Prices =1, log scale Price of services relative to goods Price of consumption relative to investment Herrendorf, Rogerson, Valentinyi 7

9 Implications of the US Evidence 1. Services value added share has been a) increasing in both final investment and final consumption expenditures; b) lower in final investment than final consumption expenditures. 2. There have been increasing trends in relative prices of a) services to goods (since 1947); b) consumption to investment (since 1980). 3. Goods and services are complements in both final expenditure categories; follows from 1.a) and 2.a). Herrendorf, Rogerson, Valentinyi 8

10 Taking Stock We have established that abstracting from structural change in investment is empirically implausible. We will now establish that abstracting from structural change in investment is not innocuous either; instead, modeling it will lead to three novel insights. Herrendorf, Rogerson, Valentinyi 9

11 Model Two-by-two-by-two structure Two production factors: capital and labor. Two sectors producing value added: goods and services. Two final-expenditure composites of sectoral value added: investment and consumption (where investment is the numeraire). Herrendorf, Rogerson, Valentinyi 10

12 Production Functions Value added Final expenditures categories Y jt = A jt K θ jt L1 θ jt, j {g, s}. X t = A xt ω 1 ε x C t = A ct ω 1 ε c x Xgt c Cgt ε x 1 ε x ε c 1 ε c + (1 ω x ) 1 ε x X + (1 ω c ) 1 ε c C ε x 1 ε x st ε c 1 ε c st ε x ε x 1 ε c ε c 1., A ct = 1: normalization. ω x = 1: investment produced entirely in goods sector. Herrendorf, Rogerson, Valentinyi 11

13 Households Life time utility 0 exp( ρt) log(c t )dt. Endowments Positive initial capital stock and one unit of time in each instant. Both capital and labor can be used in either sector. Capital depreciates at rate δ [0, 1]. Herrendorf, Rogerson, Valentinyi 12

14 Resource Constraints Production factors K gt + K st K t, L gt + L st L t = 1. Intermediate goods C gt + X gt Y gt, C st + X st Y st. Herrendorf, Rogerson, Valentinyi 13

15 A Benchmark Two-Sector Model Standard consumption-investment model from Handbook Chapter C t = à ct K θ ctl θ ct X t = à xt K θ xtl θ xt K t+1 = (1 δ)k t + X t Key results Relative price equals inverse of relative TFP s P ct P xt = Ãxt à ct Model aggregates Y t P ct C t + X t = à xt K θ t BGP exists if à xt grows at a constant rate. Along BGP, Y t grows at constant rate. Herrendorf, Rogerson, Valentinyi 14

16 Equilibrium Implications Pseudo Production Functions for Investment/Consumption Proposition 1 Along any equilibrium path, investment and consumption are produced according to the following pseudo sectoral Cobb-Douglas production functions: where A jt are effective TFPs X t = A xt K θ xtl 1 θ xt, C t = A ct K θ ctl 1 θ ct, A xt A xt ( ωx A ε x 1 gt A ct ( ω c A ε c 1 gt ) + (1 ω x )A ε x 1 εx 1 1 st, L xt X gt A gt Kt θ ) + (1 ω c )A ε c 1 εc 1 1 st, L ct C gt A gt Kt θ + X st A st K θ t + C st A st K θ t, K xt K t L xt,, K ct K t L ct. Herrendorf, Rogerson, Valentinyi 15

17 Relative Prices P st P gt = A gt A st, P ct P xt = A xt A ct. Herrendorf, Rogerson, Valentinyi 16

18 Aggregate Pseudo Production Function Y t = X t + P ct C t = A xt K θ t. Aggregate analysis of our model is like that of one sector growth model. This generalizes the two-step procedure from our Handbook Chapter: 1. solve for the consumption-investment choice; 2. solve for structural change in investment and in consumption. Herrendorf, Rogerson, Valentinyi 17

19 Implications of Households FOCs Euler Equation P ct C t = R t δ ρ. R t is the rental price of capital. Herrendorf, Rogerson, Valentinyi 18

20 Generalized Balanced Growth and Structural Change Definition A GBGP is an equilibrium path with constant rental price for capital, R t = R. This concept is less restrictive than BGP, because it permits SC. Road map (i) How does SC arise? (ii) If a GBGP exists, what properties does it have? (iii) Under what conditions does a GBGP with SC exist? Herrendorf, Rogerson, Valentinyi 19

21 (i) How does SC arise? Decomposition of sector shares P gt Y gt Y t = 1 P sty st Y t, P st Y st Y t = P ct C t Y }{{} t extensive margin P st C st + P ct C }{{} t intensive margin X t Y }{{} t extensive margin P st X st. X }{{} t intensive margin Herrendorf, Rogerson, Valentinyi 20

22 Intensive margin Standard result 1: Sectoral expenditure shares equal sectoral labor shares P st Y st P gt Y gt = L st L gt. Standard result 2: If ε x, ε c [0, 1) and  gt >  st, then P st X st P gt X gt = (1 ε x )Âgt A st > 0 and P st C st P gt C gt = (1 ε c )Âgt A st > 0. Herrendorf, Rogerson, Valentinyi 21

23 Extensive margin Prove next Along GBGP, extensive margin inactive and intensive margin determines SC. Garcia-Santana et al. (2016) Estimate and then simulate the demand system for investment and consumption. Off the GBGP, extensive margin generates hump shaped manufacturing shares. Herrendorf, Rogerson, Valentinyi 22

24 (ii) If a GBGP exists, what properties does it have? Proposition 2 If a GBGP exists, then K t = X t = Ŷ t = P ct C t = R δ ρ. Proposition 3 If a GBGP exists, ε x, ε c [0, 1), Â gt > Â st, then the shares of the services sector in total value added and total employment will increase over time. The value added share of the services sector will also increase for both final consumption and final investment. Herrendorf, Rogerson, Valentinyi 23

25 (iii) Under what conditions does a GBGP with SC exist? Proposition 4 A GBGP exists iff θa xt Kt θ 1 is constant. Same condition as in Ngai-Pissarides although now investment is a composite. Herrendorf, Rogerson, Valentinyi 24

26 Three Insights Arising from our Unified Approach Insight 1: Investment-biased technological change If  gt >  st,  xt 0, ω x > ω c, and ε ε x = ε c, then P ct P xt = Âxt A ct > 0. For previous restrictions, technological change is endogenously investment biased Related to relative-price finding of Garcia-Santana et al. (2016). Herrendorf, Rogerson, Valentinyi 25

27 Insight 2: Sectoral TFP Growth and GBGP Proposition 5. If ε x 1, a necessary condition for the existence of a BGP with structural change is that at least one of the growth rates  xt,  gt,  st is not constant. A GBGP requires constant growth of A xt = A xt ( ωx A ε x 1 gt ) + (1 ω x )A ε 1 x 1 εx 1 st If A xt,  xt,  gt,  st are all constant, then  gt =  st, which rules out structural change. This challenges common practice to impose constant sectoral TFPs (see e.g. our Handbook Chapter). We will establish below common practice is empirically implausible. Herrendorf, Rogerson, Valentinyi 26

28 Insight 3: Asymptotic Behavior of a GBGP Asymptotic behavior crucial for how SC affects productivity growth; see Duernecker, Herrendorf, Valentinyi (2017) on Baumol s Disease. Proposition 6 If a GBGP exists, ε x, ε c [0, 1),  gt >  st, lim t  gt > lim t  st, then ω x [0, 1): ω x = 1: P st Y st lim = 1 (Novel Result); t Y t P st Y st lim t Y t = P cc Y (Standard Result). Herrendorf, Rogerson, Valentinyi 27

29 Empirical Support for our Model Calibration of Model Parameters Target: nominal value added shares in nominal final expenditures. Choose: parameters to minimize squared deviations, taking as given relative prices. Find: higher goods weight in investment (expected); Leontief aggregators. ω x ω c ε x ε c Herrendorf, Rogerson, Valentinyi 28

30 Why Leontief Aggregators? CES implies relative quantities move in opposite direction from relative prices, except in Leontief case when relative quantities remain constant. Since relative price of services to goods show increasing trend, CES implies relative quantity of services to goods either decreasing or constant Real services value added over real goods value added 1947=1 Final consumption expenditure Final investment expenditure Herrendorf, Rogerson, Valentinyi 29

31 Expenditure Shares Model vs. Data 0.9 Final investment expenditure 0.9 Final consumption expenditure Services value added share 0.7 Goods value added share Data Model 0.3 Services value added share Goods value added share Data Model Herrendorf, Rogerson, Valentinyi 30

32 Formulas for Growth Accounting P jt Y jt = Â jt + R tk jt P jt Y jt K jt + W tl jt P jt Y jt L jt, X t = Â xt + P gtx gt X t X gt + P stx st X t X st. Herrendorf, Rogerson, Valentinyi 31

33 Exogenous TFPs =1, log scale Goods TFP 1.6 Services TFP 1.0 Exogenous investment-specific TFP Herrendorf, Rogerson, Valentinyi 32

34 INSIGHTS 1 and 2 Model vs. Data A xt }{{} Investment-specific TFP A xt }{{} First component (ω x A ε x 1 gt + (1 ω x )A ε x 1 εx 1 } {{ } Second component st ) =1, log scale =1, log scale Investment-specific TFP Second component First component In the model, technological change becomes endogenously investment specific in the data, the second component drives most of  xt. 2. In the model, BG with SC requires non constant TFP growth in at least one sector in the data,  xt has constant trend while  xt does not. Herrendorf, Rogerson, Valentinyi 33

35 Disaggregating Investment Natural disaggregation Equipment Structures Intellectual Property Product (software, research and development, artistic products) Herrendorf, Rogerson, Valentinyi 34

36 Expenditure Shares of Subcategories of Investment 0.7 Composition of final investment expenditure 0.7 The share of equipment in equipment and structures 0.6 Share of structures in investment Share of equipment in investment Share of intellectual property products in investmen Herrendorf, Rogerson, Valentinyi 35

37 Sector Shares in the Subcategories of Investment Final investment expenditure Final investment expenditure 1.0 Equipment 1.0 Structures Goods value added share Goods value added share Services value added share Services value added share Final investment expenditure Intellectual property products Services value added share Goods value added share Herrendorf, Rogerson, Valentinyi 36

38 Relative Prices of the Subcategories of Investment Relative price of investment expendtitures Quantity of investment =1, log scale =1, log scale 3.3 Structures relative to equipment 32 Intellectual property products Equipment Structures 1.0 Intellectual property products relative to equipment 2 Intellectual property products relative to equipment and structures Herrendorf, Rogerson, Valentinyi 37

39 Conclusion We have made two contributions Provide evidence for SC in investment. Model SC in investment and consumption taking a unified approach. Our unified approach has led to three novel insights 1. Technological change becomes endogenously investment specific. 2. BG with SC requires non constant TFP growth in at least one sector. 3. The sector with the lowest TFP growth takes over the economy asymptotically. Our next steps Model non-homotheticities in consumption. Disaggregate further. Herrendorf, Rogerson, Valentinyi 38

40 Defensive Slides Herrendorf, Rogerson, Valentinyi 39

41 Comparison with Garcia-Santana et al. (2016) Their key contributions Document facts about SC in investment for 40 countries. Estimate demand systems for investment and consumption (taking as given expenditure shares and prices without modelling production). Show that investment booms can generate hump shaped manufacturing shares. Find estimated model generates < 1/2 of increase in relative price of investment. Our key contributions Document facts about SC in investment for postwar US. Build general equilibrium model of SC in investment and consumption. Analyze and characterize GBGP, including determination of relative prices. Theoretically establish three insights and provide empirical support for two of them. Herrendorf, Rogerson, Valentinyi 40