Week 2 - Harrod Domar model Flashcards
What does the HD model focus on when it comes to growth?
Capital accumulation
What is the basic assumptions of the HD model?
- Closed economy: no flow of resources to or from the outside world, so output = income
- Can only save and spend income
What are the 2 equations for Y (aggregate income/output)
Yt = Ct + St
- aggregate income = agg C + total S
Yt = Ct + It
- agg output = value of goods produced for cons purposes + investment purposes
What does the HD model say is the binding constraint on growth?
Capital. There is an excess supply of labour.
True or false: In a closed economy, savings = investment
True (use the 2 equations for Y to prove this)
What do we assume about savings?
we assume that a fixed fraction s of income Y is saved:
St = sYt
Ct = (1-s)Yt
What is the equation for the evolution of capital stock K
K˙t = It - δK
K˙ = change in K
δ = depreciation rate
What is the role of labour in the HD model?
There is no labour in the HD model
What is the production function in the HD model?
Yt = (1/θ)Kt
What is θ?
The capital output ratio - The amount of capital required to produce a single unit of output.
θ = Kt/Yt
What is the amount of capital required to produce a single unit of output? (given as an equation)
Kt = θYt
How do you get the growth rate of output, gy? What is it
Take logs of the production function and differentiate wrt time:
gy = gk
How do you calculate the growth rate of capital, gk? What is it?
- Use It = St and St = sYt into the evolution of capital stock equation: K˙t = It - δK
- divide by Kt to get:
gk = s/θ - δ
Using the HD model, how would a country grow faster?
- Increase rate of savings s
- Decrease the capital output ratio, by increasing the rate at which capital produces output
To understand how output per capita (living standards) change, we need to include population growth in our model. Is it endogenous or exogenous?
Exogenous
What assumption do we make about the population and the labour force?
Everyone works, so population = labour force
What is the equation for labour force Lt
Lt = L0e^nt
How do we denote a variable (e.g. capital) in per worker terms?
instead of capital K, its lowercase k
How do we get the growth rate of population? what is it?
- Take logs of labour force n differentiate wrt time
gL = n
How do you get the growth rate of output per worker? Express in the growth rate of capital per worker
- write the production function in per worker terms
- Take logs n differentiate wrt time
gy = gk
How do you get the growth rate of capital per worker? What is it?
- starting from k = K/L, take logs n differentiate wrt time to get gk = gK - gL
- Subbing in from previous equations, gk = s/θ - δ - n
What is the growth rate of output per worker?
gy = gk = s/θ - δ - n
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?
- 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
Explain the savings rate s in middle income countries?
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
Explain the savings rate s in high income countries
Theres an even greater capacity for savings, but also less to aspire to. So s might drop
If we endogenise the population growth n in the HD model, how does n change with y?
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
What is HD model’s ‘knife edge’ property? What does this mean?
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.
What ratio’s does the HD model assume to be constant? Why is this a problem?
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
What would happen if population grew faster than capital?
Not enough investment to employ workers
Unemployment rises indefinitely
What would happen if capital grew faster than the population?
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
Who proposed the financing gap model
Easterly (1999)
What is the ICOR in the financing gap model?
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.
What is a countries financing gap?
Difference between the required investment rate (for a desired level of growth) and the investment rate the country can achieve on its own.
How do you calculate the required investment rate for the financing gap model? What is it?
- Decide on a desired growth rate for an economy
- Use the HD model to calculate how much investment you need to achieve this growth. Assuming 0 depreciation:
gy = s/θ - required investment rate s = gyθ
With an ICOR of 3 and a desired growth rate of 5%, what investment rate is required?
15%
Which 2 assumptions does Easterly say the financing gap model relies on (that are refuted by the data)
- Aid will go 1 for 1 into investment
- there is a fixed linear relationship between investment and growth in the short and long run
To test the 1st assumption , which OLS regression did Easterly run for 88 aid receiving countries?
invt/GDPt = B0 + B1(ODAt/GDPt) + e
invt = gross domestic investment
ODA = foreign aid (Official development assistance)
What OLS regression did he run to test the 2nd assumption?
growtht = y0 + y1(invt-1/GDPt-1+ e
where GDP growth and gross domestic investment lagged 1 period
What does Easterly show?
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
What is a criticism of Easterly?
omitted variable bias
Why is the model still used according to Easterly?
- Simple way to calculate ‘necessary’ aid which helps aid agencies rationalise foreign aid
- cost of building new model is large and benefits not internalised
- no incentives in academic literature to critically evaluate models used in practise that are not at the frontier of academic research.
