ECO362H1 Lecture Notes - Lecture 5: Capital Account, Human Capital, General Idea
Growth and Development Accounting
1 Introduction
So far, we have developed tools to analyze the causes and consequences of cross-country
differences in physical and human capital differences across countries. In this note, we now
turn our focus to the measurement of these differences in the data and how they relate (em-
pirically) to differences in output-per-capita.
Objectives:
1. Develop tools to decompose cross-country and time-series differences in income per
capita into contributing channels
2. Discuss how to data maps into the model
References:
•Mankiw, Romer and Weil (1992)
•Klenow and Rodriguez-Clare (1997)
•Weil Chapter 7
2 Data & Measurement
To motivate our discussion of data, recall that we model production in the economy as given
by
Yt=Kα
t(AtHt)1−α
1
where Ytis output; Ktis capital; Htis effective labour; Atis TFP. Recall that we take
effective labour to be given by
Ht=htNt
where htis the average level of human capital of workers and Ntis the number of workers.
In this section, we will then outline how each of these variables can be constructed using
data. In general, information on these variables can be found in the Penn-World Tables.
2.1 Output
We will measure output as the real GDP of the economy. In general, there are two consid-
erations to keep in mind for the growth and development accounting exercises:
1. Comparability across time: we want to measure output using a real variable as op-
posed to a nominal variable. This is so that we are comparing the change in quantities
over time and not also including a change in the price at which these quantities are
measured
2. Comparability across countries: similarly, we want to measure differences in quan-
tities across countries, not differences in prices. When we do cross-country comparison,
we need to ensure that we are using a common base currency to measure output.
2.2 Capital
How should we measure the capital stock Ktin the data? This is not a simple question,
as we do not directly observe capital in the data. Furthermore, even measures related to
capital in the data may not capture exactly the information that we require. For example,
one strategy of measure capital would be to add up all of the assets held by firms in the
economy. However, these assets are going to be affected by the accounting rules in the
country, which will make this measure incomparable across countries.
The solution to this problem is to use data that we are confident is measuring what we
are interested in and infer the value of capital from this measure. To be specific, we infer
the value of capital by using investment flows. This is called the Perpetual Inventory
Method (PIM).
2
The general idea of the PIM is that capital stock in any period tcan be written as
Kt=Xt−1+ (1 −δ)Kt−1
=Xt−1+ (1 −δ) [Xt−2+ (1 −δ)Kt−2]
=Xt−1+ (1 −δ)Xt−2+ (1 −δ)2[Xt−3+ (1 −δ)Kt−3]
...
=
S
X
s=1
(1 −δ)s−1Xt−s+ (1 −δ)S+1Kt−S−1
To simplify notation a bit, let’s write period t−S−1as period 0and rewrite the above
expression to be
Kt=
t−1
X
s=0
(1 −δ)sXs+ (1 −δ)tK0(1)
The above expression then states that given we know capital in period 0and the sequence
of investments {Xs}t
s=0, then we can determine capital in any period t.
However, as we stated before, we do not have a good measure of capital in period 0, so we
do not know K0. Instead, we assume that prior to period 0, investment grew at a constant
rate gX. Under this assumption, we can use (1) to find capital in period 0:
K0=
∞
X
s=1
(1 −δ)sXs=
∞
X
s=1 1−δ
1 + gX!s
X0=X0
gX+δ(2)
Note that the above expression uses the fact that X−1=X0
1+gXand so X−s=X0
(1+gX)s.
Equation (2) then states that we can approximate K0using X0as long as we have a
reasonable estimate of gXand δ. In general, we assume that the depreciation rate δis
constant and fixed over time. The growth rate of investment is then the more difficult
variable.
To estimate the growth rate of investment gX, we will assume that the growth rate of
investment prior to period 0is approximately equal to the average growth rate of investment
3
Document Summary
So far, we have developed tools to analyze the causes and consequences of cross-country di erences in physical and human capital di erences across countries. In this note, we now turn our focus to the measurement of these di erences in the data and how they relate (em- pirically) to di erences in output-per-capita. Objectives: develop tools to decompose cross-country and time-series di erences in income per capita into contributing channels, discuss how to data maps into the model. References: mankiw, romer and weil (1992, klenow and rodriguez-clare (1997, weil chapter 7. To motivate our discussion of data, recall that we model production in the economy as given by. 1 where yt is output; kt is capital; ht is e ective labour; at is tfp. Recall that we take e ective labour to be given by. Ht = htnt where ht is the average level of human capital of workers and nt is the number of workers.
