The Ghost of Finacing Gap

The main assumptions of the Financing Gap model are; that in order to achieve a desired given growth rate, investment level requirement is proportional to growth rate by a constant Incremental capital output ratio (ICOR). As well as the assumption, that in order to achieve said investment requirements, where a country’s public savings, combined with private investment are not sufficient to achieve the necessary investment level, the remainder is entitled a financing Gap. Stated, as the Aid requirement necessary for financing the given growth rate. Which Implies that this Gap must be filled by aid, in order for the required amount of growth to occur.

ICOR, the Incremental Capital Output Ratio according to Investopedia, is a measure that predicts the marginal increase in capital input required, in order to create a further unit of output, and thus create growth. When used in reference to predicting the growth of a country’s GDP a higher ICOR value is undesirable, as it can generally indicates lower efficiency of investment inputs, to outputs produced (2015).

The first testable implication of this model is that aid will be directed into investment one for one. The second being, that there is a fixed linear relationship between growth and investment in the short run.

Easterly tests the first of these implications by looking at a sample of 88 countries, to assess the degree to which aid contributions lead to one for one of above levels of investment. Using data sets on official development assistance and investment over GDP to determine which countries displayed a positive, significant relationship between aid and investment, using a coefficient of greater than or equal to one. The result of this test is discussed below. The test easterly utilises to assess the second implication mentioned is designed to access the predictive power of the linear investment to growth relationship in the short term. Regressing growth on lagged investment to GDP for 138 countries, with a median of 36 observations and a ‘zero’ constant. The same test was applied to the relationship between four-year high growth periods and which occurred within claimed necessary investment/growth level. Finally Easterly uses the equation GDP Growth per capita = (Initial Investment/GDP + Increase in Aid/GDP over initial year))/ICOR - Population growth

To access the degree to which the actual and theoretical levels of aid and investment efficiency align in their investment and GDP growth outcomes.

Easterly’s first tests find, that just 6 out of the 88 countries included in his sample showed a positive and significant with coefficients equal to, or above one. With only four of these six countries being given non-trivial amounts of aid with which to promote investment in the first place, in order to have significant impact on country growth. Thus indicating little evidence to support the testable claim that aid is directed into investment one for one. The results of the second test showed that only 4 of the 138 countries displayed a positive, significant, ‘zero’ constant relationship with an ICOP of between 2 and 5. The only country, which passed both these first tests Easterly engaged with, is Tunisia. Which seems to be an outlier with little relevance to the overall success of the model. Even with a more efficient ICOR of 2, less than half of the countries pass this test. Providing very limited support for the relationship between linear investment and growth in the short term. The test completed on four-year growth periods resulted in only 1% of countries experiencing high growth episodes whilst also fulfilling the required investment/GDP%, with an ICOP of 5. And still only 37% with and ICOP of 2. Suggesting that there is very limited evidence that investment as a percentage of GDP is a necessary condition for high growth incidences. Easterly found similarly poor percentages when testing of the necessity of investment/GDP% for increased growth episodes, was calculated. Thus not acting in support of the more general claim to fixed linear relationship between growth and investment in the short run. Easterly’s final test showed that where the financing gap model should display a one for one positive correlation between predicted and actual per capita growth, this correlation is instead slightly negative. Meaning overall these tests have failed to providing supportive evidence for the two key claims of the financing gap model. And thus seem to convincingly undermine the foundation of the Financing Gap Model.

References: Investopedia 2015, Incremental Capital Output Ratio-ICOR, Investopedia, viewed 31 July 2015, http://www.investopedia.com/terms/i/icor.asp.

Steady State

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

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

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)

plot.ts(Y)

Random depreciation

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

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

Y <- rep(NA, 200)
K <- rep(NA, 200)
K[1] <- 1
alpha <- 0.4
A <- 5
delta <- 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)

plot.ts(Y)