Heterogeneous Human Capital, Growth and Trade

Cheng-Te LeeDept. of International Trade,

Chinese Cultural University, Taiwan

Deng-Shing HuangInstitute of Economics,

Academia Sinica, Taiwan

1. Literatures/Motivations• The diversity of human capital can matter

for the POT and growth.• Diversity and Trade (Grossman & Maggie

2000AER, Grossman 2004JPE)– Labors with different talent– Industry-specific module of tasks-combination

• Conventional Industries (motor)// skill-clustering• Newly developed (software)// cross-matching

• Diversity and Growth (Das 2005)– Diversity speeds up growth

1. Literatures/Motivations (cont.)• Diversity and Trade (Grossman & Maggie 2000AER, Grossman

2004JPE)– Labors with different talent– Industry-specific module of tasks-combination

• Conventional Industries (motor)// skill-clustering• Newly developed (software)// cross-matching

– Results: Diversity Comp. Adv in Cross-Matching goods (Diversity Eff.)

• Diversity and Growth (Das 2005)– Theory: Diversity speeds up growth (if R&D is cross-matching)– Evidence: Diverse HC not necessary High Growth (Not

consistent with the real world) – (Why? Communication gap higher if HC more diverse lower

growth// Das 2005)

Real World Data

• Fact: For human capital, countries differ not only in diversity but also in Kurtosis

• Type 1: One of the countries has higher 95th/5th and higher 75th/25th than the other; for example, U.S.A. vs. Germany (denoted as DEU).

• Type 2: One of the pair countries has higher 95th/5th but lower 75th/25th than the other; for example, Canada vs. U.S.A.

Human Capital Distribution

•

Prose Document Quantitative

Coun. 95th/5th 75th/25th Coun. 95th/5th 75th/25th Coun. 95th/5th 75th/25th

CAN 2.72 1.31 CAN 3.09 1.32 CAN 2.65 1.33

AUS 2.71 1.30 CHE 2.97 1.28 AUS 2.64 1.30

USA 2.58 1.34 USA 2.90 1.36 USA 2.62 1.35

CHE 2.29 1.27 AUS 2.77 1.29 CHE 2.48 1.25

BEL 2.27 1.30 UK 2.55 1.36 IRL 2.45 1.38

UK 2.26 1.34 IRL 2.38 1.36 UK 2.44 1.37

IRL 2.24 1.33 BEL 2.16 1.28 BEL 2.35 1.32

FIN 1.78 1.24 FIN 1.95 1.27 FIN 1.82 1.23

SWE 1.75 1.23 NOR 1.80 1.23 SWE 1.77 1.23

DEU 1.74 1.24 SWE 1.77 1.24 NLD 1.76 1.21

NLD 1.72 1.22 NLD 1.74 1.22 NOR 1.72 1.21

NOR 1.65 1.19 DEU 1.72 1.22 DEU 1.67 1.21

DNK 1.55 1.19 DNK 1.69 1.23 DNK 1.65 1.20

Talent Distribution

mint

b

t2

t maxt

b2

1

b

b

2

2

t t

)(tb for Diversityεsmaller higher Kurtosis

Talent Distribution

mint

b

t2

t maxt

b2

1

b

b

2

2

t t

)(tb for Diversityεsmaller higher Kurtosis

Type 1: More diverse/ lower Kurtosis

Talent Distribution

mint

b

t2

t maxt

b2

1

b

b

2

2

t t

)(tb for Diversityεsmaller higher Kurtosis

Type 2: More Diverse and greater Kurtosis

Types of Distribution Diff.

• Type 1: a country with more diverse human capital but with lower kurtosis than its pair country (in Grossman & Maggi (2000) Grossman (2004) and Das (2005))

• Type 2: a country with more diverse human capital and higher kurtosis than the others (not yet considered in the literature) 本文

Correlation (HC Distribution, Growth Rate)

Prose Document Quantitative

Country 95th/5th* 75th/25th**

Country 95th/5th* 75th/25th**

Country 95th/5th* 75th/25th**

CAN 2.72 1.31 CAN 3.09 1.32 CAN 2.65 1.33

AUS 2.71 1.30 CHE 2.97 1.28 AUS 2.64 1.30

USA 2.58 1.34 USA 2.90 1.36 USA 2.62 1.35

CHE 2.29 1.27 AUS 2.77 1.29 CHE 2.48 1.25

BEL 2.27 1.30 UK 2.55 1.36 IRL 2.45 1.38

UK 2.26 1.34 IRL 2.38 1.36 UK 2.44 1.37

IRL 2.24 1.33 BEL 2.16 1.28 BEL 2.35 1.32

FIN 1.78 1.24 FIN 1.95 1.27 FIN 1.82 1.23

SWE 1.75 1.23 NOR 1.80 1.23 SWE 1.77 1.23

DEU 1.74 1.24 SWE 1.77 1.24 NLD 1.76 1.21

NLD 1.72 1.22 NLD 1.74 1.22 NOR 1.72 1.21

NOR 1.65 1.19 DEU 1.72 1.22 DEU 1.67 1.21

DNK 1.55 1.19 DNK 1.69 1.23 DNK 1.65 1.20

Corr 0.07 -0.13 Corr 0.17 -0.15 Corr 0.09 -0.05

Main Findings• Diversity Effect Diversity Comp. Adv. in Submodular (S-goods)

‧Pattern of Trade (more likely to Export S)

‧Growth (higher growth rate, if R&D is S-goods)

• Kurtosis Effect Kurtosis Comp. Adv. in Supermodular C-goods)

Opposite to the Diversity Effects

Theme: Kurtosis difference why an more diversity economy may have lower growth rate. (Explain the discrepancy between theoretical results and empirical observations.)

2. Model

• A small-open economy • Labor with hetero talent symmetric distribution

• 2 sectors (C&S) / 2 tasks Yi=η Fi (tx, tv) – Consumption sector C supermodular

(skill-clustering : employing identical-skill workers)

– R&D sector S submodular

（ Cross-matching: most- least-talented）

}t,tmin{)t,t(F vxvxC

}t,tmax{)t,t(F vxvxS

Model (cont.) Talent Dist.

,otherwise,0

],t,2

t[tif,b2

1

),2

t,2

t[tif,b2

b

),2

t,t[tif,b2

1

)t(

max

min

2min

btt

2max

btt

Talent Distribution

mint

b

t2

t maxt

b2

1

b

b

2

2

t t

)(tb for Diversityεsmaller higher Kurtosis

Talent Dist. & Employment

mint

b

t2

t maxt

b2

1

b

b

2

2

t t

)(tC employs labor with t around average of S employs labor of most- and least-talented

t

Approach:• Given t^ m(t^)• yc and ys solved• PPF Yc=f(Ys)• Given P=Pc/Ps• MRT= Pc/Ps• Yc/Ys• Export function• Growth rate

t̂ )ˆ(tmC sector

Case 1:

mint

b

t2

t maxt

b2

1

b

b

2

2

t t

)(tC employs labor with t around average of S employs labor of most- and least-talented

t

t̂ )ˆ(tmC sector

2/ˆmin ttt

Case 2

mint

b

t2

t maxt

b2

1

b

b

2

2

t t

)(tC employs labor with t around average of S employs labor of most- and least-talented

t

t̂ )ˆ(tmC sector

Case 1:

S S

mint

b

t 2

t maxt

b2

1

b

b

2

2

t t

)(t

)ˆ(tmt̂

C CCC

2/ˆmin ttt

C employs labor with t around average of (t)S employs labor of most- and least-talented

Case 1: 2/ˆmin ttt

)ˆ(

ˆ)ˆ22(

4)(),(

tm

tCC ttb

b

tdttttFy

)ˆ32

)(ˆ2(

4)()](,[

ˆ

min

ttb

ttb

bdtttmtFy

t

tSS

Assume: income-tax τand fully funds the new blueprints (S)

S

C

demand y

y

p

)1(

1

tt

t

ty

ty

y

y

S

C

S

C

ˆ2ˆ/

ˆ/

.

MRT

Case I (cont.)

• The export function of good S:

• (6)

• The growth rate:

• (7)

)1()]2/(1[2

)]2/(1[),,,(

22

p

tbp

ptbRDRStbp

])2

1[(4

222

pt

b

b

tg

Only b affects the growth rate.Kurtosis has no effect at all.// conventional results

Case II: Labor division for C-sector & S-sector

1. Given t^ m(t^)2. yc and ys solved3. Export function4. Growth rate

S S

mint

b

t 2

t maxt

b2

1

b

b

2

2

t t

)(t

)ˆ(tmt̂

S SCC

ttt ˆ2/

Case II (Cont.)• The export function of good S:

• (11)

• The growth rate:

• (12)

)1()1(2

),,(),,,,(

22

p

p

ptbtbp

]),,([4

)( 222

ptbb

tbg

5.02

])(4

)8(1[),,(

bt

btbtb 2),,(

21 tb

t

Both b and ε matters for growth rate.

3. More Diverse and Higher Kurtosis Talent Distribution

0 ddb

t t

)(t

More Diverse, Higher Kurtosis, POT and Growth

• Case Ι:

– POT

(14)

– Growth

(15)

tbptttt 2/12/12/ˆmin

0

dbb

ddbb

d

0

dbb

gd

gdb

b

gdg

More Diverse, Higher Kurtosis, POT and Growth

• Case II:

– POT

(16)

– Growth

(17)

tpttt 2/11ˆ2/

0)(

dbb

ddbb

d

0)(

dbg

b

gd

gdb

b

gdg

Higher b and Kurtosis (lower ε) Lower Growth rate.

4. Concluding Remarks

• More diverse and higher kurtosis talent distribution leads to change in POT and lower growth rate. (Case II)

• Kurtosis Effect dominates the diversity effect.

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