Week 2 - Harrod Domar model

Question 1

What does the HD model focus on when it comes to growth?

Answer 1

Capital accumulation

Question 2

What is the basic assumptions of the HD model?

Answer 2

1. Closed economy: no flow of resources to or from the outside world, so output = income
2. Can only save and spend income

Question 3

What are the 2 equations for Y (aggregate income/output)

Answer 3

Yt = Ct + St
- aggregate income = agg C + total S
Yt = Ct + It
- agg output = value of goods produced for cons purposes + investment purposes

Question 4

What does the HD model say is the binding constraint on growth?

Answer 4

Capital. There is an excess supply of labour.

Question 5

True or false: In a closed economy, savings = investment

Answer 5

True (use the 2 equations for Y to prove this)

Question 6

What do we assume about savings?

Answer 6

we assume that a fixed fraction s of income Y is saved:
St = sYt
Ct = (1-s)Yt

Question 7

What is the equation for the evolution of capital stock K

Answer 7

K˙t = It - δK

K˙ = change in K
δ = depreciation rate

Question 8

What is the role of labour in the HD model?

Answer 8

There is no labour in the HD model

Question 9

What is the production function in the HD model?

Answer 9

Yt = (1/θ)Kt

Question 10

What is θ?

Answer 10

The capital output ratio - The amount of capital required to produce a single unit of output.

θ = Kt/Yt

Question 11

What is the amount of capital required to produce a single unit of output? (given as an equation)

Answer 11

Kt = θYt

Question 12

How do you get the growth rate of output, gy? What is it

Answer 12

Take logs of the production function and differentiate wrt time:

gy = gk

Question 13

How do you calculate the growth rate of capital, gk? What is it?

Answer 13

1. Use It = St and St = sYt into the evolution of capital stock equation: K˙t = It - δK
2. divide by Kt to get:
   gk = s/θ - δ

Question 14

Using the HD model, how would a country grow faster?

Answer 14

1. Increase rate of savings s
2. Decrease the capital output ratio, by increasing the rate at which capital produces output

Question 15

To understand how output per capita (living standards) change, we need to include population growth in our model. Is it endogenous or exogenous?

Answer 15

Exogenous

Question 16

What assumption do we make about the population and the labour force?

Answer 16

Everyone works, so population = labour force

Question 17

What is the equation for labour force Lt

Answer 17

Lt = L0e^nt

Question 18

How do we denote a variable (e.g. capital) in per worker terms?

Answer 18

instead of capital K, its lowercase k

Question 19

How do we get the growth rate of population? what is it?

Answer 19

1. Take logs of labour force n differentiate wrt time

gL = n

Question 20

How do you get the growth rate of output per worker? Express in the growth rate of capital per worker

Answer 20

1. write the production function in per worker terms
2. Take logs n differentiate wrt time

gy = gk

Question 21

How do you get the growth rate of capital per worker? What is it?

Answer 21

1. starting from k = K/L, take logs n differentiate wrt time to get gk = gK - gL
2. Subbing in from previous equations, gk = s/θ - δ - n

Question 22

What is the growth rate of output per worker?

Answer 22

gy = gk = s/θ - δ - n

Question 23

If we endogenise the savings rate s in the HD model (make s a function of income per capita), how does s change with y?

Answer 23

• There is a subsistence level of y
• if y is low and close to this, than s will be low
• as y increases, s increases

Question 24

Explain the savings rate s in middle income countries?

Answer 24

It will be quite high due to the existence of global inequality which spurs savings in order to grow and join the club of rich countries

Question 25

Explain the savings rate s in high income countries

Answer 25

Theres an even greater capacity for savings, but also less to aspire to. So s might drop

Question 26

If we endogenise the population growth n in the HD model, how does n change with y?

Answer 26

n varies with y:
- poor countries have higher death rates (famine, disease, malnutrition, conflict), even though there are high birth rates. On balance n is low
- as y increases, death rates decrease so n increases.
- birth rates adjust to the increase in y, decreases n again

Question 27

What is HD model’s ‘knife edge’ property? What does this mean?

Answer 27

It means that the model makes some predications that are completely insane.The reason is because it relies on a fixed-coefficient, constant returns to scale production function. This means that capital and labour need to be used in fixed proportion to eachother.

Question 28

What ratio’s does the HD model assume to be constant? Why is this a problem?

Answer 28

Capital-labour, capital-output and labour-output ratio’s.

For these ratio’s to be constant, output, capital and labour all have to grow at the same rate which is unrealistic

Question 29

What would happen if population grew faster than capital?

Answer 29

Not enough investment to employ workers
Unemployment rises indefinitely

Question 30

What would happen if capital grew faster than the population?

Answer 30

Eventually all labour would be employed, labour would become the binding constraint on production.
Growth rate of output reduces to n
resources will lie idle

Question 31

Who proposed the financing gap model

Answer 31

Easterly (1999)

Question 32

What is the ICOR in the financing gap model?

Answer 32

Recalling the HD production function,
the Incremental capital-output ratio is θ.
The number of additional units of capital we need to add to get one extra unit of output.

Question 33

What is a countries financing gap?

Answer 33

Difference between the required investment rate (for a desired level of growth) and the investment rate the country can achieve on its own.

Question 34

How do you calculate the required investment rate for the financing gap model? What is it?

Answer 34

1. Decide on a desired growth rate for an economy
2. Use the HD model to calculate how much investment you need to achieve this growth. Assuming 0 depreciation:
   gy = s/θ
3. required investment rate s = gyθ

Question 35

With an ICOR of 3 and a desired growth rate of 5%, what investment rate is required?

Answer 35

15%

Question 36

Which 2 assumptions does Easterly say the financing gap model relies on (that are refuted by the data)

Answer 36

1. Aid will go 1 for 1 into investment
2. there is a fixed linear relationship between investment and growth in the short and long run

Question 37

To test the 1st assumption , which OLS regression did Easterly run for 88 aid receiving countries?

Answer 37

invt/GDPt = B0 + B1(ODAt/GDPt) + e

invt = gross domestic investment
ODA = foreign aid (Official development assistance)

Question 38

What OLS regression did he run to test the 2nd assumption?

Answer 38

growtht = y0 + y1(invt-1/GDPt-1+ e

where GDP growth and gross domestic investment lagged 1 period

Question 39

What does Easterly show?

Answer 39

For standard values of ICOR, few countries that achieve periods of high growth had met the required level or growth rate of investment as predicted by the HD model in the previous period. This suggests that investment is not even a necessary condition for growth

Question 40

What is a criticism of Easterly?

Answer 40

omitted variable bias

Question 41

Why is the model still used according to Easterly?

Answer 41

1. Simple way to calculate ‘necessary’ aid which helps aid agencies rationalise foreign aid
2. cost of building new model is large and benefits not internalised
3. no incentives in academic literature to critically evaluate models used in practise that are not at the frontier of academic research.