Expansion of Firms and Human Capital
Accumulation by Training:
A Growth Model for the Not-So-Growing
Midwest International Economics conference
Gilad Aharonovitz
Washington State University
School of Economic Sciences
October 2008
Roadmap

Introduction - development and existing
growth theory:



Endogenous growth literature
Human capital literature
Development model based on
accumulation of human capital through
on-the-job training



Model
Development phases
Extensions
Capital flows – model and empirics
 Summary

2
Introduction

Development problems and growth theory

Poverty traps are rejected: Easterly (2006, 2007)

Capital accumulation: Solow (1956)
But: Lucas (1990)

Endogenous growth literature: Romer (1990),
Grossman and Helpman (1991), Aghion and
Howitt (1992) and Aghion et al. (2001).
North-South: Krugman (1979), Acemoglu and
Zilibotti (2001).

Human capital: Mincer (1962), Becker (1964).
3
Introduction

Human capital and growth: Lucas (1988), Romer
(1989), Becker, Murphy and Tamura (1990), Stokey
(1991), Mankiw, Romer and Weil (1992), Barro
(2001), Eicher and Gracia-Penalosa (2001) and
Galor and Moav (2004)

But: schooling is about the demand for education.

Exceptions:

Galor and Tsiddon (1997)

Lucas (1988)

Burstein and Monge-Naranjo (2007), Monge-Naranjo
(2007)
4
Introduction


Motivation

Lucas (1978) acknowledges the need for managers

Firm literature (Coase, 1937, Penrose, 1959)
acknowledged the need for training.

World Bank enterprise survey – most firms train workers,
many firms regard skills of workers as an obstacle for
expansion.
This paper: on-the-job training based
development, in an environment in which the
technology and the production function are already
given, and the economy needs to utilize it.
5
The Model

Two sectors, traditional and technological.

In the technological sector, every production unit
(firm) is headed by a manager.

Firms train
profitability.

Managers can later open their own firms \ train
other managers.

managers
in
order
to
increase
Ft  Lt  M t  N :
traditional
sector’s
workers,
technological sector’s workers and tech. sector’s
managers = population size
6
The Model





Traditional sector: constant marginal productivity,
equals 1.
Technological sector: production units, y  f (l )
Standard production function.
l includes the manager. No capital.
Training managers:

Each existing unit can train managers at a cost:
c  c(m, M t 1 )
c(0, M t 1 )  0


c
 2c
c
0

0
m
 0
2
0
m
m
m
 2c
0
M t 1m
Allows to open more production units in the same period.
Newly trained managers can train after one period.
7
The Model



But: managers can leave after one period.
Managers are paid a worker’s wage at the training
period.
Timeline:




Pre-trained managers are running the firms-production
units.
Each firm decides how many managers to train (and units
to open , workers to hire)
The rest of the population work in the traditional sector,
production and consumption take place.
Example
f (l )  Al  , A 
1

m2
c( m, M t 1 )  
M t 1
8
Development Path – First Phase

The traditional sector still exists

One firm is introduced to the economy.

w=1 as long as the traditional sector exists.

l is set (diminishing marginal productivity)

Profits per firm (excluding pre-trained manager’s
wage):
 (m)  (m  1)( f (l )  w(l  1))  wm  c(m, M t 1 )

Proposition 1: Growth rate of the technological
sector is constant without externalities, and
increases over time with positive externalities.
9
Development Path – First Phase

Proposition 1: Growth rate of the technological
sector is constant without externalities, and
increases over time with positive externalities.
 (m)  (m  1)( f (l )  w(l  1))  wm  c(m, M t 1 )
 ( m)
c(m, M t 1 )
 f (l )  l 
0
m
m
c( m, M t 1 )
 f (l )  l
m

f (l )  Al  , A 
Example:
1 /(1 )
l  (A)
1

m2
c( m, M t 1 )  
M t 1
2m
 /(1 )
1 /(1 )

A
(

A
)

(

A
)
M t1
10
Development Path – Second Phase

The traditional sector disappears

Firms are hiring fewer workers – wage increases:
 N 

Wage: f ' 
 Mt 
Proposition 2: second phase growth rate is
N  Mt
Workers:
Mt

diminishing without externalities, and
diminish, stay constant, or increase
externalities.
may
with
11
Development Path – Second Phase

Since each firm is small, it can neglect its own
effect over Mt
~ ~~
~m  c(m, M )}
Max{( m  1)( f ( l )  w( l  1))  w
t 1
m
 ( m)
~ ~ ~ c( m, M t 1 )
~ ~~ ~ N
c( m, M t 1 )
 f ( l )  wl 
0
 f (l )  w
l l 
M
m
m
m



Growth rate is lower than m
Development ceases eventually (i.e., catch-up).
Example:

 1



2m
N
N
 N 
~




A


A

w  A




M 
 t
M t 1
 M t 1 (1  m) 


 M t 1 (1  m) 

m(1  m)  M t1 AN  (1   ) / 2
12
Development Path
Output and Managers throughout the Development Process
10,000,000
1,000,000
10,000
1,000
100
Managers (log scale)
Output (log scale)
100,000
10
1,000,000
1
Time
Output (total, left scale)
Managers (total, right scale)
Managers2 (total, right scale, with externalities)
Plotted for N=1,000,000 , f (l )  2l 0.8 and c( m, M t 1 )  m 2
Managers2 is plotted for N=1,000,000 , f (l )  2l 0.8 and c(m, M t 1 ) 
m2
M t0.19
13
Development Path - Extensions

Paying to be trained:





Assume bounded price / time period
Firms train more managers
Price of training is (weakly) decreasing over time
Same pattern of development.
Firm specific skills:



Firm specific skills -> one large firm.
Span of control problems / diffusion of skills
Monopolistic competition
Schooling as a pre-requisite for training.
 Heterogeneous ability

15
Evolvement of Income Inequality
Gini index throughout the Development Process
0.18
0.16
0.14
Gini Index
0.12
0.10
0.08
0.06
0.04
0.02
0.00
1,000,000
1,200,000
1,400,000
1,600,000
1,800,000
2,000,000
Output (total)
18
Capital Flows



Production function of a unit: yt  f (lt , kt )  A(lt kt
)
Firms can rent capital locally or abroad (r), agents
can save (s)

Cost of training: c(m)  Bm

Workers and capital decisions:
f (l , k )
 k (1 )  l  1  1
l

1 
2
f (l , k )
 (1   ) l  k (1 )  1  r
k
Managers’ training decision:
 (m)  (m  1)( f (l , k )  w(l  1)  rk )  wm  c(m)
 ( m)
c( m)
 f (l , k )  wl  rk 
0
m
m
19/23
Capital Flows

Capital demand:
Local supply:
K1S  0
K1D  (1  m )k
K 3S  (1  m ) s(  1)  s(  1)(1  r )
K  (1  m ) k
D
t
K 2S  s(  1)
t
t 1
K   (1  m ) i 1 s(  1)(1  r ) t 1i , t  1
S
t

i 1
Net capital position (foreign ownership):
t 1
K
NP
t
K
 (1  m ) k   (1  m )i 1 s(  1)(1  r )t 1 i , t  1
t
i 1
NP
t
t 1
1  r t 1i 

2
 (1  m )  k  (1  m ) s(  1) (
)

1

m
i 1


t

Capital flow – change in KNP

Proposition: the economy experience capital
inflows that later reverse to capital outflows.
20
Capital Flows
Net Capital Position and Net Capital Flows over Time
f (l , k )  (l 0.6k 0.4 )0.,9 c(m)  2m2 , r=0.1, s=0.2, and N>62,261
25,000
20,000
2,500
Net Capital Borrowing
(left scale)
2,000
15,000
1,500
10,000
1,000
5,000
0
500
time
-5,000
-10,000
0
-500
Net Capital Inflows
(right scale)
-1,000
-15,000
-1,500
-20,000
-2,000
-25,000
-2,500
21
Capital Flows
Net Capital Flows and Output
f (l , k )  (l 0.6k 0.4 )0.9 , c(m)  2m2 , r=0.1, s=0.2, and N>62,261
3000
2000
1000
0
0
50000
firms' output
-1000
-2000
-3000
22
Capital Flows
FDI Regression Analysis
Dependent Variable: FDIpc1990_2003
(1)
(2)
FDIpc1980_1989
1.025
(9.18)**
GDPpc1989
27.086
(3.13)**
GDPpc1989sqr
-1.411
(4.43)**
CapitalForm1980
CapitalForm1980sqr
Latitudesqr
Constant
R-square
Observations
19.517
(1.17)
0.56
69
15.110
(0.45)
0.32
76
(3)
36.417
(4.00)**
-1.486
(5.03)**
-21.742
(2.04)*
0.537
(2.65)**
-0.079
(2.49)*
203.370
(1.56)
0.49
75
23
Capital Flows
-500
0
500
1000
FDI Regression (2)
-1000
3000
2000
1000
0
0
0
-1000
50000
10
firms' output
20
30
GDPpc_1989
FDIpc1990_2003
Fitted values
-2000
-3000
24
Summary and Conclusions



This paper developed a highly stylized general
equilibrium development and catch-up model.
Mangers and firms are scarce resources in less
developed countries, the model is suitable for the
development analysis.
The analysis stresses two problems



Policy



Accumulation of human capital: training vs education
Dependence of development on behavior of firms.
Aid to the traditional sector
Supporting education
Capital flows – absorption capacity
26