technology gaps, trade and income

Technology Gaps, Trade and Income

Thomas Sampson

London School of Economics

May 2019

Thomas Sampson (LSE) Technology Gaps May 2019

Technology gaps

Productivity differences generate cross-country income inequality(Caselli 2005) and determine Ricardian comparative advantage(Ricardo 1817, Costinot, Donaldson & Komunjer 2012)

Sources of productivity variation

Allocative efficiency (Acemoglu & Zilibotti 2001, Hsieh & Klenow2009)Technology gaps (Parente & Prescott 1994, Comin & Mestieri 2018)


This paper

1 Theory of equilibrium technology gaps

Model how firm-level innovation and learning jointly shape theglobal productivity distribution and Ricardian comparativeadvantageNational innovation systems determine R&D efficiency (Nelson1993)Steady state technology gaps larger in more innovation-dependentindustries with lower advantage of backwardness and greaterlocalization of knowledge spillovers

2 How quantitatively important are technology gaps in explainingcross-country wage and income inequality?

Use R&D and bilateral trade data to estimate model and quantifywage and income variation due to technology gapsTechnology gaps account for around one-quarter to one-third ofnominal wage variation within OECD


Related literature

Endogenous comparative advantageGrossman & Helpman 1991, Redding 1999, Somale 2016

Global productivity distributionParente & Prescott 1994, Eaton & Kortum 1999, Klenow &Rodrıguez-Clare 2005, Gancia, Muller & Zilibotti 2013, Buera &Oberfield 2016

Technology adoptionCaselli & Coleman 2001, Comin, Hobijn & Rovito 2008, Comin &Mestieri 2018

Idea flows and learningLucas & Moll 2014, Perla & Tonetti 2014, Sampson 2016

Incumbent innovationKlette & Kortum 2004, Atkeson & Burstein 2010, Akcigit & Kerr2016, Konig, Lorenz & Zilibotti 2016


Environment

s = 1, . . . ,S countries, j = 1, . . . , J industries

Continuous time t , competitive markets

Labor is the only factor of production, constant population Ls

Firms differ along two dimensions: time invariant R&D capability ψand endogenous productivity θ

Firm that employs lP production workers has output

y = θ(

lP)β, 0 < β < 1


R&D

Firm can upgrade productivity through R&D or adoption. R&Dtechnology

θ

θ= ψBs

(θ

χRjs

)−γj (lR)α− δ

Bs country-level R&D efficiency. Captures absolute advantage ininnovation due to national innovation system

χRjs R&D knowledge level in country s. Captures knowledge

spillovers

γj > 0⇒ growth decreasing in current productivity relative toknowledge level⇒ advantage of backwardness (Gerschenkron1962)

lR R&D employment, δ knowledge depreciation rate, α ∈ (0,1)returns to scale in technology investment


Adoption

Adoption technology

θ

θ= BA

(θ

χAjs

)−γj (lA)α− δ

where lA denotes adoption employment

Differences from R&D technology

Firm’s R&D capability ψ does not enter the adoption technologyAdoption efficiency BA constant across countriesKnowledge level available for adoption χA

js = ηχRjs where η > 1


Knowledge spillovers

Knowledge has two components1 Domestic knowledge depends on domestic productivity frontier θmax

js(excluding firm’s own productivity)

2 Global knowledge depends on global knowledge capital χj

χRjs =

(θmax

js

) κj1+κj χ

11+κjj

Localization of knowledge spillovers increasing in κj > 0

R&D spillovers generate growth in global knowledge capital

χj

χj=

S∑s=1

Mjs

∫ψλjs(ψ)lRjs (ψ)dG(ψ)

where Mjs denotes mass of firms and{λjs(ψ)

}determines the

strength of R&D spillovers


Closing the model

Representative consumer in each country with unit intertemporalelasticity of substitution and discount rate ρ

Final consumption good is Cobb-Douglas aggregate acrossindustries with expenditure shares µj

Within industries output is differentiated by country of origin withArmington elasticity σ

Iceberg trade costs τjss to export from s to s

Free entry with initial (ψ, θ) drawn from joint distribution amongincumbent firms

Firms face exogenous exit shock at rate ζ

Details


Balanced growth path

Firm opts for R&D rather than adoption if capability ψ exceeds

ψ∗js = ηγjBA

Bs

Threshold ψ∗ decreasing in R&D efficiency Bs, but increasing inadvantage of backwardness γj

Technology gaps (i.e. relative productivity levels) are stationaryand balance dispersion and concentration forces

Dispersion: R&D capability, R&D efficiency, localization ofknowledge spilloversConcentration: Advantage of backwardness, global knowledgespillovers

Productivity distribution in industry j shifts outwards at rate gj in allcountries and all firms in steady state with productivity growth rategj Details Firm steady state


Equilibrium technology gaps

Average technology gap between countriesEθ∗ 1

1−β

js

Eθ∗ 1

1−β

j s

1−β

=

Bs

Bs

(Ψjs

Ψj s

) γj (1−β)

1+κj−α

1+κjγj

where Ψjs is average effective capability accounting for adoptionbeing equivalent to R&D with capability ψ∗js. Ψjs decreasing in Bs

Ψjs =

∫ ψmax

ψ∗js

ψ1

γj (1−β)−α dG(ψ) +(ψ∗js

) 1γj (1−β)−α G(ψ∗js)

Technology gap increasing in Bs and Ψjs, but Ψjs decreasing in Bs

Define innovation-dependence of industry j as the elasticity ofaverage technology gap to R&D efficiency


Comparative advantage

Balanced growth path exports from s to s in industry j given by

log EXjss = υ1j + υ2

s − (σ − 1)(log ws + log τjss

)+ (σ − 1)

1 + κj

γj

[log Bs +

(γj(1− β)

1 + κj− α

)log Ψjs

]where υ1

j and υ2s are endogenous industry and destination terms

PropositionOn a balanced growth path, countries with higher R&D efficiency havea comparative advantage in more innovation-dependent industrieswhere the advantage of backwardness is low and the localization ofknowledge spillovers is high


International income inequality

Income per capita is increasing in R&D efficiency and under freetrade

∂ log ws

∂ log Bs=σ − 1σ

J∑j=1

νjsInnovation-dependencejs

where∑J

j=1 νjs = 1

PropositionOn a balanced growth path with free trade, the elasticities of wages,income per capita and consumption per capita to R&D efficiency areweighted averages of industry innovation-dependence levels

Trade costs complicate analysis, but leave intuition unchangedDetails


Quantifying technology gaps

Estimate model to obtain

Country R&D efficiency levels from within-industry variation in R&DintensityIndustry innovation-dependence levels from bilateral trade patterns

Calibrate model and quantify differences in wages and incomesdue to observed variation in R&D efficiency

Estimate under first order approximation that is valid when fewfirms perform R&D. 9.9% UK goods firms invested in R&D in2008-09

Approximation implies innovation-dependence given by

IDj =(1− β)κj

γj(1− β)− α


R&D efficiency

Industry-level R&D intensity

RDjs =α(δ + gj)

ρ+ ζ + γj(δ + gj)

k[γj(1− β)− α

]k[γj(1− β)− α

]− 1

η−kγj

(Bs

BA

)k

Estimate bs = k log Bs from relative R&D intensity acrosscountries

bs =1

Ns

2014∑t=2010

20∑j=1

log(

RDjst

RDj st

),

RDjs is ratio of R&D expenditure to value-added from OECD datafor 25 countries and 20 manufacturing industries

Estimates


Estimating innovation-dependence

Estimate IDjk from bilateral trade data

log(

EXjss

EXj ss

)− (σ − 1) log

(ws

ws

)= −(σ − 1)

IDj

kbs

− (σ − 1) log τjss + εjss

Parameterize trade costs as function of distance, border, commonlanguage, free trade agreement and exporter-industry fixed effect

Set σ − 1 = 6.53 from Costinot, Donaldson & Komunjer 2012Include controls for other determinants of

Comparative advantage: interaction of industry dummy variableswith physical capital abundance, human capital, rule of law,financial developmentProductivity: institutional quality, business environment

Use pooled trade data 2010-14 for 22 ISIC 2 digit goods industriesEstimates Model validation


Calibration

Calibrate model for 25 OECD countries in 2012

22 goods industries plus non-tradable services. Assumeinnovation-dependence is zero in services

Solving for relative wages and incomes does not require fullcalibration, e.g. do not need to calibrate R&D spillovers λjs(·)

Calibrate: R&D intensity, population, industry expenditure shares,firm exit rate, profit share, trade elasticity, discount rate Details

Compare equilibria with and without R&D efficiency differences toobtain nominal wage and real income variation due to R&Defficiency


Nominal wages

AUS

AUT BEL

CAN

CHL

CZE

DEUDNK

ESP

FIN

FRA

GBR

HUN

IRLITA

JPN

KOR

MEX

NLD NOR

POL

PRT

SVN

TUR

USA

-.8-.6

-.4-.2

0.2

Cal

ibra

ted

log

wag

e

-2 -1.5 -1 -.5 0 .5Log nominal wage

Elasticity of calibrated wages to observed wages equals 0.30

Ratio of standard deviations of calibrated and observed log wagesequals 0.36 Robustness


Real incomes

AUS

AUTBEL

CAN

CHL

CZE

DEUDNK

ESP

FIN

FRA

GBR

HUN

IRLITA

JPN

KOR

MEX

NLD NOR

POL

PRT

SVN

TUR

USA-.3

-.2-.1

0.1

Cal

ibra

ted

log

GD

P p

er c

apita

-1 -.5 0 .5Log GDP per capita

Elasticity of calibrated to observed GDP per capita is 0.14 and standarddeviation ratio is 0.19


Conclusions

Develop theory of how innovation and adoption determinetechnology gaps and income levels

Industries with lower advantage of backwardness and higherknowledge localization are more innovation-dependent

Estimate R&D efficiency and innovation-dependence from R&Dand trade data and use to calibrate model

Technology gaps account for around one-quarter to one-third ofnominal wage variation within the OECD


Intertemporal preferences

Representative consumer in each country has intertemporalpreferences

U(t) =

∫ ∞t

e−ρ(τ−t) log c(τ)dτ

ρ > 0 discount rate

Budget constraint

a(t) = ιs(t)a(t) + ws(t)− zs(t)c(t)

a per capita assetsιs interest ratews wagezs price of final consumption


Demand

Final consumption good is Cobb-Douglas aggregate acrossindustries with expenditure shares µj

Within industries output is differentiated by country of origin withArmington elasticity σ

Iceberg trade costs τjss from s to s

Export value from s to s in industry j given by

EXjss = τ−σjss

(pjs

Pj s

)1−σµjzscsLs

where pjs is price of industry j output produced in country s andPj s is industry price index


Entry

Free entry determines mass of firms Mjs

Entrant must hire f E workers to create unit flow of new firms

Entrants draw initial (ψ, θ) from joint distribution Hjs(ψ, θ) ofcapability and productivity among incumbent firms

Firms face exogenous exit shock at rate ζ

Parameter restriction1

1− β> γj >

α

1− β+

κjγj

1 + κj

⇒ Firms’ intertemporal optimization problems concave

Set global consumption expenditure as the numeraireS∑

s=1

zscsLs = 1

Back


Balanced growth path properties

Let gj be the growth rate of global knowledge capital χj .Necessary conditions for a balanced growth path

Productivity distribution Hjs(θ) shifts outwards at rate gj in allcountriesKnowledge levels χR

js , χAjs grow at rate gj in all countries

Output prices decline at rate gj , nominal wages time invariantInterest rate ιs = ρ constant across countries and over time

Output and consumption per capita grow at rate q =∑J

j=1 µjgj in allcountries

Back


Firm steady state properties

1 Steady state relative productivity and R&D investment increasingin capability ψ if perform R&D

2 R&D intensity independent of firm size, decreasing in γj ,increasing in gj

ws lR∗js (ψ)

pjsy∗js(ψ)=

α(δ + gj)


3 Adoption equivalent to R&D with capability ψ∗js4 Within-country firm size inequality increasing in α and β,

decreasing in γj

θ∗js(ψ′)

θ∗js(ψ)=

(ψ′

ψ

) 1−βγj (1−β)−α

, ψ′ ≥ ψ ≥ ψ∗js(ψ′

ψ∗js

) 1−βγj (1−β)−α

, ψ′ ≥ ψ∗js ≥ ψ

1, ψ∗js ≥ ψ′ ≥ ψ

Back


R&D problem

Firm chooses R&D investment to maximize expected presentdiscounted profits net of R&D costs

maxφ,lR

∫ ∞t

e−(ρ+ζ)(t−t)ws

1− ββ

(βpjsχ

Rjs

ws

) 11−β

φ− lR

dt

subject to the R&D technology where φ ≡(θ/χR

js

) 11−β denotes

productivity relative to the R&D knowledge level

Firm’s optimization problem is a discounted infinite-horizon optimalcontrol problem with state variable φ and control variable lR

Solving the optimal control problem implies each firm has aunique steady state which is saddle-path stable


Firm steady state & transition dynamics

lR

φ

φ = 0

lR = 0

lR∗js (ψ)

φR∗js (ψ)

Stable arm


Steady state

Steady state relative productivity

φR∗js (ψ) =

αβ β1−β (Bsψ)

1α

(pjsχ

Rjs

ws

) 11−β (δ + gj)

α−1α


α

γj (1−β)−α

Steady state R&D employment

lR∗js (ψ) =

(δ + gj)(φR∗

js (ψ))γj (1−β)

ψBs

1α


Firm steady state under adoption

Adoption problem isomorphic to R&D problem

Adoption problem has unique steady state with

φA∗js =

αβ β1−β

(Bsψ

∗js

) 1α

(pjsχ

Rjs

ws

) 11−β (δ + gj)

α−1α


α

γj (1−β)−α

where φ ≡(θ/χR

js

) 11−β

Adoption investment intensity equals R&D intensity of firms thatperform R&D

ws lA∗js

pjsy∗js=

α(δ + gj)


Back


General equilibrium

Balanced growth path wages ws, assets as and growth rates gjsatisfy

Ls =J∑

j=1

µj

ρ+ ζ

(ζ + βρ+

αρ(δ + gj

)ρ+ ζ + γj

(δ + gj

))Zjs

asLs =J∑

j=1

µj

ρ+ ζ

(1− β −

α(δ + gj

)ρ+ ζ + γj

(δ + gj

))wsZjs


General equilibrium

gj =S∑

s=1

µjα(δ + gj

)ρ+ ζ + γj

(δ + gj

) Zjs

Ψjs

∫ ψmax

ψ∗js

λjs(ψ)ψ1

γj (1−β)−α dG(ψ)

where:

Zjs ≡S∑

s=1

τ1−σjss (ρas + ws) Lsw−σs

BsΨ

γj (1−β)

1+κj−α

js

(σ−1)(1+κj )

γj

∑Ss=1 τ

1−σj ss w1−σ

s

BsΨ

γj (1−β)

1+κj−α

j s

(σ−1)(1+κj )

γj

Back


R&D efficiency

AUS

AUTBEL

CAN

CHL

CZE

DEU

DNK

ESP

FIN

FRA

GBR

HUN

IRLITA

JPN

KOR

MEX

NLD NOR

POL

PRT

SVN

TUR

USA

-3-2

-10

Log

R&D

effi

cien

cy

9.5 10 10.5 11Log GDP per capita

Back


Innovation-dependence

0103

1012

13

1415

16

17

18

19

20

21

22

2324

25

26

27

28

2930

3133

.2.3

.4.5

.6In

nova

tion-

depe

nden

ce

-5 -4 -3 -2 -1Log Share of firms that perform R&D

Back


Model validation

Undertake two validation exercises

1 Firm-level R&D investment Details

2 Out-of-sample test Details

Back


Firm-level R&D

Model implies

1FiRDj

= − 1αk log η

log ShRDjs −log(BA/Bs

)α log η

+ρ+ ζ

α(δ + gj)

FiRDj is R&D intensity conditional on performing R&DShRDjs is share of firms that perform R&D

Compute FiRDj and ShRDjs from UK Annual Business Survey andBusiness Expenditure on R&D survey 2008-09


Validation test

0103

0508

1012

13

14

15

16

17

18

19

20

21

22

23

2425

26

27 28

29

303133

050

100

150

1 / (

R&D

inte

nsity

of f

irms

that

per

form

R&D

)

1 2 3 4 5Negative Log Share of firms that perform R&D

Back


Out-of-sample test

Use innovation-dependence estimates to perform out-of-sampletest of model’s comparative advantage predictions

Sample: 9 European countries with Eurostat R&D intensity data

Estimate

log(

EXjss

EXj ss

)−(σ−1) log

(ws

ws

)= ξCompAdvj s +Controlsjss +εjss,

where CompAdvj s = −(σ − 1)IDjk log bs and other controls are

same as baseline specification

Model predicts ξ = 1

Estimate ξ = 0.74 with standard error of 0.06

Back


Parameter values

Structural estimates: R&D efficiency, innovation-dependence,trade costs

UK firm-level surveys: R&D intensity conditional on performingR&D

OECD data: population, industry expenditure shares, exit rate

β = 0.85 implies 15% profit share (Gabler & Poschke 2013, Barkai2017)

σ − 1 = 6.53, ρ = 0.04

Back


Robustness checks

Baseline GDP per capita

Homogeneous innovation‐dependence

Low trade elasticity

Moderate trade

elasticity

High trade elasticity

Industry trade

elasticities(a) (b) (c) (d) (e) (f) (g)

Elasticity 0.300 0.279 0.300 0.305 0.310 0.283 0.238Standard deviation ratio 0.363 0.331 0.353 0.366 0.369 0.345 0.304

Elasticity 0.144 0.125 0.156 0.123 0.135 0.141 0.141Standard deviation ratio 0.195 0.167 0.208 0.167 0.182 0.192 0.197

Average 0.316 0.277 0.295 0.340 0.324 0.306 0.379Standard deviation 0.113 0.123 0.348 0.184 0.091 0.258Correlation with baseline 0.924 0.848 0.945 0.974 0.548

(iv) Trade elasticity 6.53 6.53 6.53 2.5 4.5 8.5 IndustryRow (i) gives the elasticity of calibrated log wages to observed log nominal wages, and the ratio of the standard deviation of calibrated log wages to the standard deviation of observed log nominal wages. Row (ii) gives the same statistics for real income per capita. Row (iii) reports summary statistics on the innovation‐dependence estimates for goods industries used in the calibration. Correlation with baseline is the correlation with the baseline estimates used in column (a). Row (iv) shows the trade elasticity used in the calibration. Column (a) uses estimates from Table 1, column (c) to calibrate the model. For column (b) innovation‐dependence is estimated including the interaction of industry dummy variables with the importer's log GDP per capita as an additional control. In column (c) innovation‐dependence is restricted to be the same in all goods industries. Industry‐specific trade elasticities used for column (g) from Caliendo and Parro (2015).

(i) Nominal wage

(ii) Real income per capita

(iii) Innovation‐dependence

Table 2: Calibration results

Back


Income & comparative advantage

-1.5

-1-.5

0.5

120

00 in

com

e el

astic

ity

-2 -1 0 1 21962 income elasticity

Estimate sectoral income elasticity βj of exports for 2 digit SITC sectors from

EXjs = αs + δj + βj GDPPCs + εjs


Industrial development & comparative advantage

05

1019

62-2

000

expo

rt gr

owth


China

-6-4

-20

24

1962

-200

0 ex

port

grow

th


Japan

-50

510

1519

62-2

000

expo

rt gr

owth


Korea-5

05

1019

62-2

000

expo

rt gr

owth


Singapore-5

05

1019

62-2

000

expo

rt gr

owth


Taiwan

-50

510

1962

-200

0 ex

port

grow

th


Thailand


Income elasticities & industry characteristics

1516

17

1819

20

2122

23

24

2526

27

2829 30

31

3233

34

35

36

-1-.5

0.5

Inco

me

elas

ticity

-7 -6 -5 -4 -3R&D intensity

1516

17

1819

20

2122

23

24

2526

27

2829 30

31

3233

34

35

36

-1-.5

0.5

Inco

me

elas

ticity

10 11 12 13Capital intensity

1516

17

1819

20

2122

23

24

2526

27

2829 30

31

3233

34

35

36

-1-.5

0.5

Inco

me

elas

ticity

.2 .3 .4 .5 .6Skill intensity


technology gaps, trade and income

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