ECO362H1 Lecture Notes - Lecture 6: Human Capital, Capital Accumulation, Indian Council Of Medical Research
Human Capital
1 Introduction
Up to now, we have laid out the basic framework and discussed how the model accounts for
capital differences across countries. As Figure 1 shows, there are also substantial differences
in human capital across countries.
Figure 1: Human Capital Differences
NGA
ZWE
ROU
HKG
ESP
MUS
MEX
CIV
HTI
RWA
MWI
GRC
GAB
FJI
COL
IND
UGA
GHA
FIN
MDG
ZMB NAM
SYR
NIC
USA
EGY
ISR
SEN
LUX
NOR
MAR
BEN
CYP
TGO
MYS
PAK
PHL
DZA
PAN
HND
JAM
AUT
VEN
TTO
ECU
CAF
URY
BRA
CMR
ZAF
CHE
ETH
NPL
JOR
GMB
COD
SWE
TWN
MRT
ISL
FRA
KOR
IRN
SGP
TUN
MLI
NZL
LKA CHL BEL
MOZ
LSO
ITA
PRY
SLV
BRB
MLT IRL
GBR
AUS
TZA
COG
PRT
DNK
KEN
IDN
JPN
GTM
NLD
BFA
DEU
ARG
THA
DOM
PER
CRI
CAN
BWA
BOL
TUR
BGD
BDI
CHN
NER
0 .5 1 1.5
Human Capital (log)
6 7 8 9 10 11
Output per Capita (log)
In this note, we will extend the model to account for differences in human capital across
countries. We begin with the simplest framework in which household invest and accumulate
human capital similarly to physical capital. As we will see, the underlying intuitions in the
model are retained from the simple case.
Objectives:
1
1. Discuss what human capital measures
2. Extend the Neoclassical Growth model to include human capital
References:
•Weil Chapter 6
2 Human Capital
We first need to discuss what is meant by human capital. Broadly, we will take human
capital to be a composite measure of the attributes of individual workers that determine
their productivity. For example, human capital includes an individuals:
•Education - formal education, training, on-the-job learning, etc;
•Health - nutrition, physical well-being, access to medicine, etc.
For our purposes in this note, we will treat human capital htas being a composite measure
of the above factors. That is, we make the simplifying assumption that human capital can
be converted into a single variable.1As such, we will tend to think of human capital as being
equivalent to education.
Types of Investment: Before going to the model it is useful to think about how household
invest into human capital. We may broadly group investment into human capital into two
categories: time and expenditure. We may think of time investment as capturing the time
individuals spend improving their human capital - e.g. time going to school, research or going
to the gym. On the other hand, we may think of expenditure investment as investment into
infrastructure that improves the quality of human capital gained from a fixed time investment
- e.g. quality of education or healthcare. Both dimensions of investment are important in
practice.
In this note we will develop two seperate models that emphasize one of the two types
of investment.2Because expenditure investment is qualitatively similar to investment into
1This is equivalent to assuming that there is some underlying process in which households optimally
decide on the choice of each sub-group based on some aggregate investment into human capital. Intuitively,
this would be thought of as deciding human capital in two steps: (1) choose investment into all types of
human capital; and (2) decide how to allocate this investment across uses.
2We could of course build a model that incorporates both types of investment, but this would be compli-
cated and would not add much insight.
2
physical capital it is left as optional.
Accumulation of Human Capital: We model human capital as a stock of knowledge that
determines the relative contribution of workers to production. In general, we will take the
human capital accumulation equation to be
ht+1 = (1 −δh)ht+ft(xh
t, nt, ht)
where δh∈(0,1) is the depreciation of human capital and f(·)is a human capital production
function. We can interpret δhas the decline in human capital over a period if no new human
capital was produced. For example, this could be a result of new household not receiving
education.
The production of new human capital can depend on expenditure xh
tand time nt. Im-
portantly, these two channels will have different implications for how human capital is accu-
mulated in different countries.
3 Time Investment
We will begin by describing both the household’s and firm’s problem before defining and
characterizing the equilibrium.
Household: Households have log-utility over consumption given by
∞
X
t=0
βtlog(ct)
The household begins with a stock of capital k0and stock of human capital h0. The
physical capital accumulation equation is as in general model:
kt+1 = (1 −δ)kt+xt(1)
where δ∈(0,1) is the depreciation rate of capital.
Human capital accumulation depends on the amount of time the household spends im-
proving its human capital (i.e. in education). The human capital accumulation equation is
3
Document Summary
Up to now, we have laid out the basic framework and discussed how the model accounts for capital di erences across countries. As figure 1 shows, there are also substantial di erences in human capital across countries. In this note, we will extend the model to account for di erences in human capital across countries. We begin with the simplest framework in which household invest and accumulate human capital similarly to physical capital. As we will see, the underlying intuitions in the model are retained from the simple case. 1: discuss what human capital measures, extend the neoclassical growth model to include human capital. We rst need to discuss what is meant by human capital. Broadly, we will take human capital to be a composite measure of the attributes of individual workers that determine their productivity. For example, human capital includes an individuals: education - formal education, training, on-the-job learning, etc, health - nutrition, physical well-being, access to medicine, etc.
