Dynamic Transition and Economic Development

Ping WangDepartment of Economics

Washington University in St. Louis

January 2017

1

A. Introduction

1. The big picture

! Prior to 1800: output/consumption per capita and wage rate were roughlyconstant over time

! After 1800: all these aggregateswere growing over time

! By measuring output (Y) by realfarm land rent and wage (W) byreal farm wage, we observe thefollowing (Hansen-Prescott 2002):

! For example, UK GDP per hour(1985 US$) increased 22 timesfrom 1780 to 1989 (populationincreased only 5 times from 11 to 57 millions):1700 1780 1820 1890 1938 1960 1989

0.82 0.84 1.21 2.86 4.97 8.15 18.35

2

2. A closer look at five economies (Ngai 2004)

3

3. The speed of transition to modern growth (increasing over time)

! It took Netherlands/UK/US/Canada (early development) 65/55/45/35 years togrow from $2,000 to $4,000 (in 1990 US$)

! It took Korea and Taiwan (taking off in mid-1960s) only 15/10 years toaccomplish such a transition

4

4. Literature:

! Matzuyama (1992): increasing returns and development! Lucas (1993): LBD and development (Philippines vs. Korea/Taiwan)! Goodfriend-McDermontt (1995) and Hansen-Prescott (2002): early

development! Laitner (2000): saving and transition to modern growth! Gollin-Parente-Rogerson (2003): transition from agriculture to manufacturing! Kongsamut-Rebelo-Xie (2002): transition from agriculture to manufacturing

and to service! Parente-Prescott (1999) and Ngai (2004): barriers to modern growth! Atkeson-Kehoe (2007): technological revolutions and economic transition! Acemoglu-Guerrieri (2008): nonbalanced growth and dynamic transition! Chang-Wang-Xie (2009): skill accumulation, endogenous technology

advancement and transition to modern growth! Gollin-Lgakos-Wugh (2012) and Lagakos-Waugh (2013): agricultural

productivity gaps! Koren-Tenreyro (2013): technological diversification and growth stabilization! Rodrik (2015): deindustrialization (hump-shaped manufacturing sector share)

5

B. Early Development: From Malthus to Solow: Hansen-Prescott (2002)

! Basic Idea: extending Laitner (1998) and using specific-factor setup (land inagriculture) to analyze the transition from agriculture to manufacture

1. The Model

! 2-pd OG: the young own labor; the old own capital and land! Production (2 sectors: M, S, 3 factors: K, N, L)

" Multhus:" Solow:" γi > 1; S K-intensive (θ > φ); K fully depreciated; L no depreciation

! M and S are perfect substitutes! Preference: ! Budget constraint:

! Population growth:

6

2. Optimization and Equilibrium

! Firms: ! Consumers: max U subject to BCs! Market clearing: (capital)

(labor)(land)(goods MBC)

3. Main Findings

! YM > 0 (specific factor L > 0 + Inada); YS > 0 if

! Consumption (Diamond 1965):! Intertemporal no-arbitrage: ! Theorem: t < 4 s.t. YS > 0 (diminishing return to land)! Numerical example: γM = 1.032 and γS = 1.518! Main shortcomings:

" Perfect substitution between M and S, limiting a number of rich results" 2-period OG: difficult to analyze shorter run dynamic transition

7

C. The Role of Agriculture in Development: Gollin-Parente-Rogerson (2003)

! Extending Hansen-Prescott (2002) by allowing separate consumption in M andS and by considering infinite horizon setup

1. The Model

! Production (K as a specific factor in m):

" ;

" ;

! Preference: V = , with

where is the subsistence level of food consumption

8

2. Equilibrium

! Optimization is trivial as a result of specific factor and subsistenceconsumption

! Equilibrium labor allocation:

! Numerical analysis (calibrating U.K.): γm = 1.013, θ = 0.5, δ = 6.5%, α =0.0001, β = 0.95, { , γa} s.t. Na(1800) =35% and Na(2000) = 5%

3. Main Findings

! staged development of countries(flying geese)

! long/slow process of earlydevelopment, with late comersgrowing faster

! Aa = 1, 0.19 and 0.05 => transitionto modern growth started in 1750, 1850 and 1950, respectively.

9

D. Technological Revolutions and Economic Transition: Atkeson-Kehoe (2007)

! A tale of two revolutions: " the second industrial revolution:

1860-1900" the recent information technology

(IT) revolution: 1970-2000! Extending the job turnover and

organizational capital setups ofHopenhyne-Rogerson (2003) andAtkeson-Kehoe (2005) with carefulmodeling of technology diffusion

! Key assumptions:" new plants embody new technologies" improvements in technologies for

new plants are on-going" new plants improve technologies

through gradual learning

10

1. The Model

! Preference: U =

! Budget constraint:

! Plant-level production (PP): " one manager is required with γ = span of control (Lucas 1978), paid wm,

with a fraction φ operating new plants" variable inputs, capital (k) and labor (l), are freely mobile, paid r and w" z and A measure economy-wide and plan specific technologies" operating plants draw independent innovations ε to A, with probability πs,

depending on age (or year of establishment, s)" θ is used for scaling plant rent" plant-level organization capital = (A, s), with initial level (τt, 0), where τt is

the frontier blueprint for a plant that is built in t-1 and starts in t

! Final good (numeraire) output:

" λ = measure of plants (fixed due to fixed number of managers)

11

! Final producer optimization: demand for q = ! Plant optimization:

" factor demands: s.t. (PP)

" new plant decision:

- hire a manager to build a new plant at t if 0

- if it is so decided, the new plant starts operating in t+1; otherwise,maintain the existing plan

2. Equilibrium and Results

! capital market clearing: ! labor market clearing: ! manager market clearing:

(new plants’ managerial demand + existing plants’ managerial demand = 1)! final goods market clearing:

12

! Age-dependent cutoff At*(s):

" a plant (A, s) with A At*(s)

continues operating" a plant (A, s) with A < At

*(s)stops operating and exits

" life cycle of plants are plotted! Diffusion of plant-embodied

technologies can be measured bythe fraction of labor hired in plantsof age k and younger,

which is the sum over the fraction of labor hired in plant of age s (denoted lt,s)! Plant productivity and size:

" Aggregate productivity: " Aggregate cohort productivity: " Plant size: " : higher relative cohort productivity <=> larger cohort

13

3. Calibration

! The model is calibrated to yield reasonable fit with the data with a slowincrease in productivity growth and slow diffusion of new technology:

! Future work:" industry-specific technology diffusion" trade and international technology diffusion" skill accumulation and technology switches

14

E. Technological Diversification and Growth Stabilization (Koren-Tenreyro 2013)

! After taking off, countries usually grow at highly volatile rates; eventually,growth stabilizes

! This paper highlights technology diversification in variety inputs as the driverfor reduced growth volatility in the longer run

1. The Model

! CES aggregate production:

where

" A (TFP) > 0 and ε > 1 (Pareto substitute)" χ = productivity shock, variety i specific" l = labor, with total labor force = L

15

! A productivity shock arrives following a Poisson process J with arrival rate γand jump size χ:

" productivity is 1 prior to the arrival and jumps to 0 after the first arrivalof dJ > 0

" this implies:

! Under symmetry, " n = #operative varieties" l(j,t) = total labor by firm j" so, (only #operative varieties matters)

16

! CES aggregator implies iso-elastic demand: ! Labor demand: ! Operating profit:! Technology adoption:

" new prospective entrants with n = 0 pay I(0)=κL units of the final good perunit of time to adopt the first technological variety, arriving at Poissonrate η

" upon paying I(j) units of the final good, incumbent firm j adopts a newvariety whose (Poisson) arrival rate is given by f(I(j)/L, n(j)) (CRTS)- L captures negative competition effect- n captures positive current knowledge effect (Klette-Kortum 2004)- denote as adoption intensity of a size-n firm, so

, where g is the inverse of f(.,1)! Mass of firms:

" = measure of firms with k operative varieties" firm-size mass distribution follows a

Markov process with deterministic trends F and jumps G:

,

17

! Stochastic dynamics of n:

" μ(0) = η, μ(n) = λn = f(I(n)/L,n) for n>0" J+ is a Poisson process governing the success of adoption – inflows" Ji is the Poisson process of the productivity shock (jumping to zero at

arrival rate γ) – outflows! Household lifetime utility: (Euler equation => r(t) = ρ)! To ensure positive growth and finite firm value, we impose:

! Firm value:

s.t. the laws of motion of and n(t)" only two intensive margin decisions: pricing and adoption investment" two states (n, )" flow profits discounted at rate r = ρ

18

! Bellman equation:

" flow profits" changing state with increased varieties from n to n+1" changing state with productivity shock losing a variety (n drops to n-1)" changing state with productivity for nonoperative varieties" changing state due to deterministic trend

! FOCs w.r.t. p and I:

" aggregate productivity is given by function A(N, m0) > 0, increasing in#operative firms N but decreasing in #new entrants m0

" markup is decreasing in n

19

! Free entry: V(0, ) = 0

! Aggregate number of varieties:

! Goods market equilibrium: , where

! Functional income distribution:

2. Equilibrium

! Firm value: , with per variety value given by " firm value is linear in n

! Adoption intensity:

" adoption intensity is independent of n! Wage and output: and

" per capita profit per variety depends on λ (not n)" both wage and output are linear in N

20

! Mass of new entrants m0 satisfies:

! Mass of incumbent firms is Markow with:

" λ(i-1)mi-1 firms successfully adopt variety i (inflows into i)" λimi-1 firms successfully adopt variety i+1 (outflows from i)" ηm0 new entrant firms successfully enter variety 1" if any of the first i varieties fail due to productivity shock (dJk>0), size i

becomes size i-1 (outflows) and size i+1 becomes size i (inflows)" if variety i+1 fails, they becomes size i (inflows)" nonoperative ones remain unchanged

21

3. Main Findings

! Expected sales growth of firm of size n:

" = rate of successful adoption - rate of failure due to productivity shock! Variance of sales growth of firm of size n:

" increasing in adoption success and productivity failure, but decreasing in n! Expected aggregate growth:

" increasing in new entrants m0 but decreasing in N

! Variance of aggregate output:

" depending on sectoral weight " is a measure of technological concentration

! A more advanced economy have more varieties to hedge against productivityshocks (technological diversification), thus reducing growth volatility" as Y , growth variance goes to 0 (LR asymptotic BGP)

! Open issues: " sectoral heterogeneities in production (higher volatility)" shifts in preferences (higher volatility)

22

F. Nonbalanced Growth and Dynamic Transition: Acemoglu-Guerrieri (2008)

! Transition to modern growth usually features nonbalanced growth between thetwo sectors

! Conventional optimal growth models focus only on balanced common growth! To permit nonbalanced growth, it requires balancing between nonbalanced

growth sectors:" Kongsamut-Rebelo-Xie (2002): growing service sector offsets shrinking

agriculture sector" Bond-Trask-Wang (2003): 2 nonbalanced growth sectors (producing

physical and human capital) offset each other" Acemoglu-Guerrieri (2008): 2 nonbalanced growth sectors (producing

intermediate goods) offset each other

1. The Model

! Preference:

! Labor is supplied inelastically, equal to the population, growing at rate n

23

! Production: " final good: Y(t) = , ε < 1

" intermediate goods:

- sector 2 is more capital intensive ( )- M1 and M2 grow at rates m1 > 0 and m2 > 0

! Resource constraint: , where ! Factor allocation constraints: ,

2. Equilibrium

! Final good competitive profit condition:

! Intermediate goods demand:

! Factor allocation conditions:

" labor:

" capital:

24

! Factor shares in sector 1:" labor:

" capital:

! Sector 1 intermediate output share:

! Factor prices: w(t) = , R(t) = r(t) + δ =

! Results:κ Y1/Y w/R σk = RK/Y

K (capital stock) + - + -

M2 (capital-biased technology) + - - -

3. Dynamics toward Asymptotic Growth

! Assumptions:" and ε < 1 (sector 1 is asymptotically dominant)" (bounded growth)

25

! Asymptotic factor shares: ! Nonbalanced growth rates:

" n*, z*, zi* = asymp. growth rates of labor, capital, sector-i capital" g*, gi*, gc* = asymp. growth rates of output, sector-i output, consumption

! Results (define ω = α2(m2/α2 - m1/α1) > 0):" saddle-path stability" κ* = 1: sector 1 continues capital-deepening, eventually absorbs all capital" (per capita consumption growth)" : aggregate output and sector-1 output/capital

all grow at the same rate as aggregate consumption" asymptotic constant interest rate and aggregate capital share" main finding: faster growth of employment and slower growth of output

in labor-intensive sectors:- , : sector-2 capital grows at slower

rate than aggregate output, whereas sector-2 output grows at fasterrate than aggregate output

- : sector-1 labor grows at the same rate asoverall employment, but sector-2 labor grows at a lower rate

26

4. Calibration (U.S. 1948-2005)

! Industry capital intensities:

! More labor-intensive industries have faster employment growth and sloweroutput growth

27

! Sector-1 labor/capital shares, interest rate and aggregate capital share intransition: 1948-2098

28

! Model fitness:

" aggregate capital income shares and sectoral output ratios are best-fitted" model-predicted employment ratios decline not as sharp in as the data

over 1948-2005

! Future work:" different industrial skill composition" different industrial organization capital

29

G. Deindustrialization: Rodrik (2015)

! In many developed and even developing countries (including most LatinAmerican and some Asian countries), there has been a fast rise of the serviceindustry accompanied by a decline in the manufacturing industry

! Such a deindustrialization, sometimes called hollowlization of themanufacturing industry, has raised concerned by policymakers

! It consequences for jobs and wages also have political ramifications

1. A Simple Illustration

! Two sectors: manufacturing (m) and nonmanufacturing (n)! Total labor supply = 1, with a share of α in the manufacturing sector

! Production:

! Using “hat” notation, demand changes under constant elasticity of substitutionare captured by:

30

! Labor mobility => (VMPL)! Goods market clearing: and where x = net exports

in manufactured goods and nonmanufacturing trade is balanced or nontraded

2. Comparative statics

! Manufacturing employment share:

where

(< 1 under trade deficit)" rising trade deficit (dx < 0) => lower manufacturing share" under inelastic demand (σ < 1) with not too large trade deficit (λ > σ),

manufacturing share is decreasing in manufacturing technical progressbut increasing in nonmanfacturing technical progress

31

! Manufacturing output share :

" even when the manufacturing employment share may decline as a result ofdifferential TFP growth, the manufacturing output share may change verylittle or even be higher

" indeed, we can simplify the above expression to:

so with inelastic demand, the manufacturing output share rises with differential TFP growth

32

3. The Case of Small Open

! Export price is exogenous and x is pinned down by world demand:

" the manufacturing employment share now rises with differential TFPgrowth, but is lower when the world price of the manufactured good falls

4. Open Questions

! Can these factors explain cross-country trends?" disaggregate sectoral changes" nonhomothetic preferences and production" Hansen-Vizcaino-Wang (2017)

! Shall we be concerned with deindustrialization?" trade protection" labor reallocation during hollowlication" immigration of low skilled workers