Part 1 - The Ghost of the Financing Gap

What are the main assumptions of the “Financing Gap model”?

The Harrod-Domar-Chenery Two Gap Model or the “Financing Gap Model” is based on two main assumptions. The first of these states that the investment required for a country to achieve a certain growth rate is proportional to the growth rate by the constant known as the ‘Incremental Capital Output Ratio’ (ICOR). Secondly, the gap between required investment and the sum of private financing and domestic saving in a given country is known as the “Financing Gap”, this is the aid requirement.

What is the ICOR?

The ICOR (Incremental Capital Output Ratio) is the ratio at which a change in capital will be able to change GDP within a country. A high ICOR suggests that the country has inefficient production, and is in essence inefficiently using its capital.

\(ICOR = \Delta K / \Delta Y\)

What are the testable implications of the Financing Gap model?

Two testable implications can be derived from the models initial assumptions. These testable implications propose that all aid provided will go towards investment one for one. And that there is a fixed linear relationship between growth and investment in the short run.

How does Easterly test them?

Easterly tests the effectiveness of the aid to investment from the 88 aid countries present in the data set. This is done by comparing the dependent variable of Investment/GDP and the independent variable of Overseas Development Assistance, to establish whether a coefficient greater than or equal to one is present.

Secondly, Easterly assesses the linear growth-investment relationship. This is done by analysing the short-run link between a coefficient of growth on investment and GDP, allowing the model to display if it can predict growth with a constant ICOR (predictive power).

Easterly also looks at whether investment is necessary in the short-run to help developing countries. This was done by assuming a certain ICOR, being either 2, 3.5 or 5, and analysing the growth that occurs on average when investment is present. It was then tested what the change would be should increased investment be allocated to countries with said ICOR’s. This allows us to understand what would occur if the Financing Gap model had correct outcomes, compared to a more conservative approach.

What does he find?

The effectiveness of the Financing Gap model show that when testing the aid to investment ratio, only 6 of the 88 countries, or 7%, displayed a coefficient greater than or equal to one that was significantly positive. The remaining groups all saw either non-significant positive coefficients or negative coefficients.

The predictive power found through the second set of testing undertaken again displays that very few countries in this data set were able to meet all conditions of Easterly’s tests. In order to pass these tests, countries were required to show a positive and significant relationship between growth and investment, hold a constant insignificantly different to zero, as well as an ICOR between 2 and 5. Only 3% of all 138 countries were found to meet these conditions, while another 5% were able to meet the conditions baring an ICOR between 2 and 5.

Having assessed the predicted outcomes of required investment on GDP, Easterly was able to view how accurate the model has been. With the constant settings of ICOR’s compared to the average yearly and 4 year growth that was anticipated by the model, countries predicted to boom including Zambia and Chad have seen to be growth disasters. As a result, Easterly concludes that the correlation of actual and predicted growth is slightly negative, suggesting that the model does a poor job to predict growth well.

Part 2: Computation Task

Steady State

\(Y_{t} = A \times K^{ \alpha}_{t-1}\)

\(K_{t} = s \times Y_{t} + (1-\delta) \times K_{t-1}\)

Y<-rep(NA,200)
K<-rep(NA,200)
K[1]<-1
alpha<-0.4
A<-5
delta<-0.07
s<-0.3
Y[1]<-A*K[1]^alpha
for (t in 2:200)
  {Y[t]<-A*K[t-1]^alpha
  K[t]<-s*Y[t]+(1-delta)*K[t-1]}
plot.ts(K)

Variable Stock Depreciation

\(Y_{t} = A \times K_{t-1}^\alpha\)

\(K_{t} = s \times Y_{t} + (1-\delta_{t}) \times K_{t-1}\)

Y<-rep(NA,200)
K<-rep(NA,200)
K[1]<-1
alpha<-0.4
A<-5
delta<-rnorm(200,0.07,0.05)
s<-0.3
Y[1]<-A*K[1]^alpha
for (t in 2:200)
  {Y[t]<-A*K[t-1]^alpha
  K[t]<-s*Y[t]+(1-delta[t])*K[t-1]}
plot.ts(K)