The first main assumption of the financing gap model is that in order for a country to achieve a target growth rate, it requires a given level of investment proportional to (a constant) Incremental Capital Output Ratio.

The second main assumption of the financing gap model is that this given level of investment can be achieved through the provision of aid to ?fill the gap? between the required level of investment and the cumulation of a country?s private financing and domestic savings.

If these assumptions hold, it seems reasonable to assume that it is possible to accurately estimate the investment requirements of a particular country and provide it financial aid sufficient to meet this.

The Incremental Capital Output Ratio (ICOR) is a measure designed to predict the marginal amount of capital required in order to increase output by a single unit. In the financing gap model, the constant that relates the required level of investment to the growth rate is one over the ICOR. Having a higher ICOR (or lower constant) means a larger amount of capital is required to achieve the production of an additonal unit of output. As a result, according to the Financing Gap Model, countries with a higher ICOR will require more investment to achieve a given level of growth.

Easterly identifies two testable implications of the Financing Gap Model.

That aid goes into investment on a one-for one ratio. Or, if you like, the provision of aid will have no immediate and direct impact on the level of consumtion.

That there is a fixed, linear relationship between growth and investment in the short-run. The linear constant in this relationship is one over the ICOR.

- Aid to Investment
- Easterly tests this implication using data from 88 countries with observations over a period of 30 years from 1965. He regresses Investment on the Overseas Develoment Assistance (ODA) received (with both variables expressed as a portion of GDP). According to the results of his regression, only six countries show a positive and significant relationship that is greater than or equal to 1. Of these, two had received small enough amounts of ODA that they may be considered outliers. Easterly clearly considers this evidence against the model. It is worth noting here that he does acknowledge the clear endogeneity of such a basic model, circumventing this problem somewhat with the qualification that he is merely testing whether these two variables ?evolve? in a way that might be expected by it?s advocates.

- Investment to Growth
- In order to test the hypothesis that the relationship between investment and growth is linear and constant, Easterly regresses growth on lagged investment to GDP (presumably a single, one year lag, although he does not specify) and a constant (one over an unchanging ICOR). He does this for a sample of 138 countries with a minimum of 10 observations of both growth and (lagged) investment. He then tests the significance of both lagged investment and the constant (allowing him to test the constancy of the relationship across time). His results show that only 11 countries present a significant and positive co-efficient for lagged investment. Of these, only 7 do so with the third, constant variable being insignificantly different to zero. Furthermore, only 4 of these countries do so with an ICOR between 2 and 5.

\(Y_{t}=AK_{t-1}^\alpha\)

\(K{t}=sY_{t}+K_{t-1}(1-\delta)\)

\(A=5\)

\(s=0.3\)

\(\delta=0.07\)

\(\alpha = 0.4\)

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

`plot.ts (y)`

\(\mu=0.07\) \(\sigma = 0.05\)

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

`plot.ts(y)`

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