Technology Adoption, Capital Deepening, and International Productivity Differences

Transcription

1 Technology Adoption, Capital Deepening, and International Productivity Differences Chaoran Chen University of Toronto October 25, / 59

2 Introduction Stylized Facts A Model with Technology Adoption in Agriculture Calibration Quantitative Analysis Appendix 2 / 59

3 Introduction Why agriculture? Rich-poor productivity differences are much larger in agriculture: GDP: 214-fold; Non-agriculture: 44-fold; agriculture: 488-fold Agricultural employment share is much higher in poor countries: US 31%; poor countries: 633% If all countries have the US level of agricultural labour productivity: Rich-poor GDP per capita: 21-fold Large literature studies agricultural productivity differences, but a substantial portion remains unexplained I propose a new explanation: Rich-poor differences of agricultural technology adoption Technology adoption is key to accounting for observed facts in agricultural capital intensity 3 / 59

4 Facts Novel data on sectoral capital intensity: rich-poor differences in capital intensity are larger in agriculture Historical data on the US: capital-output ratio is constant in non-agriculture but increases in agriculture; massive mechanization in agriculture Mechanization happened in the US at a certain stage of development Poor countries have not mechanized their agriculture and the agricultural capital intensity is lower 4 / 59

5 Research Question Why poor countries have not mechanized their agriculture? How do differences in technology adoption affect capital intensity and agricultural productivity? Use US mechanization process as a benchmark to study the lack of mechanization in poor countries Have a framework to vary the level of development and frictions 5 / 59

6 In This Paper Build a two-sector GE model with mechanization (modeled as technology adoption) in agriculture Modern technology: more capital intensive; Traditional technology: more labour intensive Economic development: capital is cheaper and the modern technology replaces the traditional one 6 / 59

7 In This Paper Build a two-sector GE model with mechanization (modeled as technology adoption) in agriculture Modern technology: more capital intensive; Traditional technology: more labour intensive Economic development: capital is cheaper and the modern technology replaces the traditional one Calibrate it to the historical data of the US economy for 100 years Quantitative analysis: Technology adoption is key to accounting for the lower agricultural capital intensity in poor countries; amplifies the rich-poor differences in agricultural productivity 6 / 59

8 In This Paper Build a two-sector GE model with mechanization (modeled as technology adoption) in agriculture Modern technology: more capital intensive; Traditional technology: more labour intensive Economic development: capital is cheaper and the modern technology replaces the traditional one Calibrate it to the historical data of the US economy for 100 years Quantitative analysis: Technology adoption is key to accounting for the lower agricultural capital intensity in poor countries; amplifies the rich-poor differences in agricultural productivity Differences in level of developments explain two thirds of the rich-poor gaps in capital intensity and agricultural productivity Land market frictions are also important in discouraging mechanization 6 / 59

9 Related Literature Introduce technology adoption to agricultural productivity literature: Gollin-Parente-Rogerson (2002, 2005), Restuccia-Yang-Zhu (2008), Adamopoulos (2011), Lagakos-Waugh (2013), Adamopoulos-Restuccia (2014), Donovan (2014), Tombe (2015), Gottlieb-Grobovšek (2015), Caunedo-Keller (2016), Chen (2016), etc Also related to: Misallocation: Restuccia-Rogerson (2008), Guner-Ventura-Xu (2008), Hsieh-Klenow (2009), etc Technology adoption: Parente-Prescott (1994), Comin-Hobijn (2004, 2010), Ayerst (2016), etc Long-run growth: Hansen-Prescott (2002), Ngai (2004), Gollin-Parente-Rogerson (2007), Yang-Zhu (2012) 7 / 59

10 Introduction Stylized Facts A Model with Technology Adoption in Agriculture Calibration Quantitative Analysis Appendix 8 / 59

11 Cross-Country Fact My novel dataset for sectoral capital intensity Capital: aggregate from PWT 63, agriculture from World Bank Price adjustment: Restuccia-Urrutia (2001) Sectoral value-added: WDI data and FAO data Price adjustment: Gottlieb-Grobovšek (2015) Employment: PWT 63 and FAO data Calculate K-Y ratio and K-N ratio 9 / 59

12 Cross-Country Fact Rich-poor differences of capital intensity are wider in agriculture Capital-output ratio: Non-agriculture: 21-fold; agriculture: 32-fold Capital-labour ratio: Non-agriculture: 10-fold; agriculture: 165-fold 10 / 59

13 Cross-Country Fact Rich-poor differences of capital intensity are wider in agriculture Capital-output ratio: Non-agriculture: 21-fold; agriculture: 32-fold Capital-labour ratio: Non-agriculture: 10-fold; agriculture: 165-fold Consistent with evidence on agricultural technology Comin-Hobijn (2004) Tractor-per-farmer: 360-fold More Evidence 10 / 59

14 Historical Facts of the US The capital intensity of the US agricultural sector increases over time Nominal Capital-Output Ratio Agriculture Non-Agriculture Year 11 / 59

15 Historical Facts of the US The usage of modern machinery increases over time Trucks Tractors Grain and bean combines Pickup balers Mower conditioners 12 / 59

16 Introduction Stylized Facts A Model with Technology Adoption in Agriculture Calibration Quantitative Analysis Appendix 13 / 59

17 Overview of the Model Build on the neoclassical growth model Two sectors: agriculture and non-agriculture Agriculture: heterogeneous farmers to fit the adoption curve; to study the role of misallocation Non-agriculture: representative firm A representative household allocates its members to be farmers and workers; decides on consumption and investment Three goods: Agricultural good: for consumption only; Non-agricultural good: for consumption and investment; Investment-specific technology: 1 unit of non-agr good υ t units of capital good 14 / 59

18 Agricultural Technologies Two technologies available to farmers: traditional VS modern Traditional Technology: y = Aκs 1 α r γ r k α r l γ r Modern technology: y = AκBs 1 α m γ m k α m l γ m Modern technology has a higher capital share αm > α r Modern technology incurs a fixed cost: f units of capital good Indivisibility of equipment, up-front investment in learning, or the required infrastructure of modern technology 15 / 59

19 Technology Adoption Farmers are heterogeneous in their ability s Span-of-control: high-ability farmers operate larger farms Choose modern technology if and only if π m (s) π r (s) = sω p k f π π r π m p k f 0 π m p k f s 16 / 59

20 Technology Adoption Farmers are heterogeneous in their ability s Span-of-control: high-ability farmers operate larger farms Choose modern technology if and only if πm (s) π r (s) = sω p k f Threshold of adoption: ŝ = pk f Ω π π m π m p k f π r p k f 0 ŝ s 17 / 59

21 Technology Adoption Farmers are heterogeneous in their ability s Span-of-control: high-ability farmers operate larger farms Choose modern technology if and only if πm (s) π r (s) = sω p k f Threshold of adoption: ŝ = pk f Ω π π m π m p k f π r p k f 0 ŝ s 18 / 59

22 The Non-agricultural Sector A representative firm produces the non-agricultural goods according to Y n = A K α n Ñ 1 α n 19 / 59

23 The Household s Problem The household allocates its members to be workers and farmers Workers: same wage income w from a representative firm; Farmers: heterogeneous farm profits π(s) I assume no selection 20 / 59

24 The Household s Problem Utility: U = β t[ ϕ log(c at ā) + (1 ϕ) log(c nt ) ] N t, t=0 Budget constraint: (p t c at +c nt )N t +pt k x t = N nt w t (1 ξ)+ π t (s)f (ds)n at +pt k r t k t +q t L+T t s S Capital accumulation: k t+1 = (1 δ)k t + x t π, where π is the barrier to investment t, 21 / 59

25 Definition of the Equilibrium Given K 0, the competitive equilibrium consists sequences of consumption bundles and investments {c at, c nt, x t } t=0, farm inputs and outputs {k t(s), l t (s), y t (s), s S} t=0, prices {p t, pt k, w t, r t } t=0, inputs and outputs of the representative firm { K nt, Ñ nt, Y nt } t=0, aggregate capital stock in the economy {K t } t=0, and agricultural employments {N at} t=0, such that Given the prices, interest rates and wages, the representative household maximize its utility by choosing the optimal level of consumption and investment as well as the optimal employment share in agriculture: {c at, c nt, x t, k t+1, N at } t=0 Given the prices, interest rates and wages, the representative firm in the non-agricultural sector maximizes its profit by choosing { K nt, Ñ nt } t=0 Given the prices and interest rates, farms choose the optimal level of inputs and outputs {k t (s), l t (s), y t (s), s S} t=0 22 / 59

26 Definition of the Equilibrium All markets clear: Agricultural good: Non-agricultural goods: Capital market: Labour market: N at c at N t = N at s s y t (s)f (ds), c nt N t + x t υ t = Ỹ nt, t t k t (s)f (ds) + K nt = K t = k t, N at Land market: N at s F (ds) + Ñ nt = N t, s l t (s)f (ds) = L, t t t 23 / 59

27 Equilibrium Conditions: Static Denote c t = p t c at + c nt The indirect utility function is ũ(c t, p t ) = log(c t p t ā) ϕ log p t + log(ϕ ϕ (1 ϕ) 1 ϕ ) Total income of the household: (N t N at )w t (1 ξ) + s S π t (s)f (ds)n at + p k t r t k t + q t L + T t Labour allocation requires s S π t(s)df (s) = w t (1 ξ) Total income can be written as N t w t (1 ξ) + p k t r t k t + q t L + T t 24 / 59

28 Equilibrium Condition: Dynamic The household s problem can be re-written as max c t,x t,k t+1 β t ũ(c t, p t ) = β t[ ] log(c t p t ā) ϕ log p t, t=0 t=0 st c t N t + p k t x t = N t w t (1 ξ) + p k t r t k t + q t L + T t, k t+1 = (1 δ)k t + x t π Similar dynamics as the neoclassical growth model 25 / 59

29 Long Run Growth The model aggregates similarly to a one-sector neoclassical growth model Asymptotic balanced growth path: interest rate is asymptotically constant: [ gc g ] v r ABGP = π β (1 δ) Ongoing structural change with asymptotic balanced growth: Non-homothetic term (ā): resources move from agr to non-agr Agricultural employment share: N at N t ( c ) = ϕ + F A at Investment-specific technology υ t plays a larger role: Increases economy-wide labour productivity (Greenwood et al, 1997); Benefits the modern technology more than the traditional one 26 / 59

30 Technology Adoption over Time Two forces contributes to technology adoption over time: Aggregate factors: TFP and investment-specific productivity are growing over time Capital becomes relatively cheaper than labour Structural transformation Labour move out of agriculture larger farm sizes 27 / 59

31 Introduction Stylized Facts A Model with Technology Adoption in Agriculture Calibration Quantitative Analysis Appendix 28 / 59

32 Roadmap Strategy: match the model to the US time series between 1900 and 2000 Step 1: Determine the values of the parameters FIXED over time: Preferences: { c, ϕ, β}; Technologies: {αr, α m, γ r, γ m, δ}; Ability distribution: F (s) Step 2: Determine the TIME SERIES (level and growth rate): Endowments: {N t, L t }; Economy-wide productivity {At } and investment technology {υ t }: (calibrated to the non-agricultural sector) Agricultural specific productivity {κt } Step 3: Adoption parameters (best fitting the adoption curve): Adoption curve: Traditional-tech Bt and adoption cost f t 29 / 59

33 Technologies Traditional: capital share 010, labour share 06, land share 030 Gollin-Parente-Rogerson (2007) Modern: capital share 036, labour share 046, land share 018 Valentinyi-Herrendorf (2008) The key channel in my model requires α m > α r 30 / 59

34 Ability Distribution The ability s S follows a lognormal distribution with mean 0 Its standard error is calibrated to the distribution of farm value-added of the US at the year 2007 (both model and data) Value Added, Cumulative Data Model Farm Percentile, Small to Large 31 / 59

35 Productivities υ t : price of the investment goods Moment: the relative price of investment and durable goods over consumption non-durable goods and services, from BEA υt : grows at 101% per year Relative Price, Year 2000 = Data Trend Year 32 / 59

36 Productivities The economy-wide productivity A t : Yn N n increased for 69-fold between 1900 and 2000 The agriculture specific productivity κ t : Y a N a increased for 304-fold between 1900 and / 59

37 Technology Adoption Data: farms with major machines farms with modern technology; Moment: % output produced by farms with modern technology; f t and B t : tech adoption in the model best matches the data Technology Adoption Rate Data Model Year Aggregate Production Function 34 / 59

38 Calibration: Summary Category Parameter Value Moment Technology α r 010 Capital share (traditional technology) γ r 025 Land share (traditional technology) α m 036 Capital share (modern technology) γ m 018 Land share (modern technology) α n 033 Capital share (non-agricultural sector) δ 004 Depreciation rate π 1 Normalization Preferences c 0055 Agricultural employment share in 2007 ϕ 0003 Long-run agricultural employment share β 096 K/Y ratio of 3 (non-agricultural sector) Ability σ s 1327 Farm size distribution in 2007 Endowments L 1900, L , 1 Farming land N 1900, N , 1 Population Productivity υ 1900, υ , 1 Relative price of investment goods A 1900, A , 1 Non-agricultural labour productivity κ 1900,κ , 1 Agricultural labour productivity Tech Adoption f 1900,f , 002 Adoption curve B 1900,B , 25 Adoption curve 35 / 59

39 Model Fit over Time (Not Targeted) Capital-output ratio: 4 Capital-Output Ratio Agr, Data Non-agr, Data Agr, Model Non-agr, Model Year Other Time Series 36 / 59

40 Introduction Stylized Facts A Model with Technology Adoption in Agriculture Calibration Quantitative Analysis Appendix 37 / 59

41 Quantitative Analysis: Aggregate Factors Step 1: If we fit into the model the differences of aggregate factors across countries, how is the model s prediction compared to the data? Aggregate factor differences (parameters VS moments): Land endowment (L) land-labour ratio; Barrier to investment (π) non-agr capital-output ratio; Economy-wide TFP (A) non-agr labour productivity What does the model predict for agricultural moments? 38 / 59

42 Aggregate Factors: Explain 2/3 of the Rich-Poor Gaps Data Model Explained Agriculture: Capital-output ratio % Capital-labour ratio % Labour productivity % Non-agriculture (targeted): Capital-output ratio Labour productivity Whole Economy: GDP per capita % 39 / 59

43 Aggregate Factors: Explain 2/3 of the Rich-Poor Gaps Data Model Explained Agriculture: Capital-output ratio % Capital-labour ratio % Labour productivity % Non-agriculture (targeted): Capital-output ratio Labour productivity Whole Economy: GDP per capita % Technology adoption rate decreases to around 26% (compared to around 10% from CHAT dataset) Average farm size is 30-fold smaller than in the US 39 / 59

44 Aggregate Factors: Explain 2/3 of the Rich-Poor Gaps Data Model Explained Agriculture: Capital-output ratio % Capital-labour ratio % Labour productivity % Non-agriculture (targeted): Capital-output ratio Labour productivity Whole Economy: GDP per capita % Technology adoption rate decreases to around 26% (compared to around 10% from CHAT dataset) Average farm size is 30-fold smaller than in the US Decomposition: A accounts for 65% of labour productivity differences; π 24%; L 7% 39 / 59

45 Technology Adoption Channel Data Full Model No adoption Agriculture: Capital-output ratio Capital-labour ratio Labour productivity Non-agriculture (targeted): Capital-output ratio Labour productivity Whole Economy: GDP per capita Model without technology adoption: capital-output ratio: opposite in direction; deteriorate in other moments 40 / 59

46 Technology Adoption Channel Technology adoption amplifies agricultural productivity differences: affects agricultural capital intensity; directly affects the sectoral TFP of agriculture 41 / 59

47 Technology Adoption Channel Technology adoption amplifies agricultural productivity differences: affects agricultural capital intensity; directly affects the sectoral TFP of agriculture Model s prediction with/without technology adoption: Y a 1 α γ = A 1 a N a ( Ka ) α ( 1 α γ L ) Y a Y a γ 1 α γ 41 / 59

48 Technology Adoption Channel Technology adoption amplifies agricultural productivity differences: affects agricultural capital intensity; directly affects the sectoral TFP of agriculture Model s prediction with/without technology adoption: Y a 1 α γ = A 1 a N a ( Ka ) α ( 1 α γ L ) Y a Y a γ 1 α γ Y a ( ) α 1 α γ Ka Y a N a : 156-fold; A 1 1 α γ a : 123-fold; : 156/123=127-fold 41 / 59

49 Technology Adoption Channel Compare US with poor countries: the differences in the economy-wide TFP plays three roles in agriculture: directly affects agricultural productivity; affects agricultural capital intensity through adoption; affects agricultural (endogenous) sectoral TFP through adoption 42 / 59

50 Technology Adoption Channel Compare US with poor countries: the differences in the economy-wide TFP plays three roles in agriculture: directly affects agricultural productivity; affects agricultural capital intensity through adoption; affects agricultural (endogenous) sectoral TFP through adoption Traditional wisdom of development accounting: Klenow-RodriguezClare (1997): Y N = ( ) α K 1 α Y A In this context: ( ) K Y is not independent of A Capital share α is not exogenous 42 / 59

51 Technology Adoption Channel So far all neoclassical power: aggregate factors account for two-third of observed differences in capital intensity and agricultural productivity Credit frictions are not likely to be important Consistent with evidence from field experiments: Pingali, 2007; Kaboski-Townsend, 2012; Karlan et al, / 59

52 Distortions Step 2: Beyond neoclassical power Aggregate factors do not explain all the difference Literature suggests land misallocation may be an obstacle to agricultural development Banerjee-Iyer (2005), Adamopoulos-Restuccia (2014, 2015), Gottlieb-Grobovšek (2015), Chen (2016), etc Model untitled land in the economy on top of differences of aggregate factors 44 / 59

53 Untitled Land Farmers allocated equal amount of land; no land market Rich-Poor Differences Data Model AF Only w/ Unt Land Agriculture: Capital-Output Ratio Capital-Labour Ratio Labour Productivity High ability farmers have little incentive to adopt the modern tech Similar mechanism: land ceilings, progressive taxation on farm size Aggregate factors + misallocation can explain most of the differences 45 / 59

54 Long-Run Growth and Convergence Step 3: When will poor countries mechanize their agriculture? Suppose US and poor countries grow at the same rate Aggregate factor differences held constant Tech adoption parameters fixed at the 2000 level 46 / 59

55 Long-Run Growth and Convergence Adoption Rate Poor w/ untitled land Poor no untitled land United States Year Agr Productivity Year Agr Productivity Difference (US/Poor) Year 47 / 59

56 Conclusion Rich-poor differences in capital intensity are larger in agriculture than in the non-agricultural sector Technology adoption is key to accounting for the lower agricultural capital intensity in poor countries temporarily amplifies agricultural productivity differences Differences in level of developments explain two thirds of the rich-poor gaps in capital intensity and agricultural productivity Land market frictions are also important in discouraging mechanization 48 / 59

57 Cross-country Fact Rich-poor differences of capital intensity are wider in agriculture Real Capital Output Ratio (US=1) Non Agriculture Agriculture Nominal Capital Output Ratio (US=1) Non Agriculture Agriculture GDP Per Capita (US=1) GDP Per Capita (US=1) Back to Introduction 49 / 59

58 Cross-country Fact Rich-poor differences of capital intensity are wider in agriculture Real Capital Labour Ratio (US=1) Non Agriculture Agriculture GDP Per Capita (US=1) Back to Introduction 50 / 59

59 Cross-country Fact ( I regress the difference of capital-output ratio log( Ka Y a log Kn Y )it n on a )it country s GDP per capita Dependent My Constructed Data WIOD Data Variable K/Y (1) (2) (3) (4) (5) (6) Log GDP 066** 031** 043** 056** 041** 019 (003) (009) (003) (007) (003) (014) Time Dummy Country Dummy Measure of K/Y Nominal Nominal Real Real Nominal Nominal Back to Introduction 51 / 59

60 Tractors Per Farmer Tractor Per Farmer (US=1) GDP Per Capita (US=1) Back to Introduction 52 / 59

61 Land Endowment Land endowment is not the key determinant of capital usage in agriculture (The correlation is not significant) Capital Output Ratio (US = 1) Arable Land Per Capita (US = 1) Back to Introduction 53 / 59

62 Land Endowment Fact A1: land endowment is not the key determinant of capital usage in agriculture Table : Tractors across Countries Country Arable Land Tractors Per Per Farmer 1000 Farmers UK Japan Korea India Philippines Back to Introduction 54 / 59

63 Estimating the Aggregate Production Function Aggregate production function in agriculture may be CES where capital and labour are more substitute than Cobb-Douglas I estimate the following simultaneous equation group Y t = [θ k (exp(γ k t)k t ) ρ + θ n (exp(γ n t)n t ) ρ ] 1 ρ ; (1) r t = θ k [ exp(γ k t) K t Y t ] ρ Yt K t ; (2) w t = θ n [ exp(γ n t) N t Y t ] ρ Yt N t (3) using simulated time series data from my model to get γ k, γ n, and ρ Test H 0 : ρ = 0; H 1 : ρ > 0 55 / 59

64 Estimating the Aggregate Production Function Parameter My Paper HHV (2015) ρ 0396*** 0368 (0024) γ k 0003*** 0023 (0001) γ l 0015*** 0050 (0001) Back to Calibration 56 / 59

65 Model Fit over Time (Not Targeted) The agricultural employment share: Agricultural Employment Share Data Model Year 57 / 59

66 Model Fit over Time (Not Targeted) The agricultural employment share: Value Added in Agriculture Data Model Year 58 / 59

67 Model Fit over Time (Not Targeted) Labour productivity: Labour Productivity, Year 1900 = Agr, Data Non-agr, Data Agr, Model Non-agr, Model Year Back to Calibration 59 / 59