To provide a comparison between binary recursive trees and more standard multivariate analysis, vve begin by reporting the probit estimates (where the dependent variable equals unity for fast growth observations):
The probit (which predicts 68 percent of the observations correctly) identifies investment, inflation, population growth, human capital, and black market exchange rate premia (as well as the “catch-up” term, and drought or war conditions) as “significant” determinants of rapid economic growth. But it does not reveal whether, for example, the effects on inflation on growth depend upon the level of investment, or whether investment has any positive effect on growth in countries engaged at war. To address that type of question, we turn next to binary recursive trees.
The first tree, based on a classification of observations into the top-third versus the bottom-third growth rates, is depicted in figure 1. The overall quality of the rules embodied in the tree can be evaluated by their ability to divide the test sample into high and low growth observations. Seventy-five percent of the low growth observations and almost seventy percent of the high growth observations were correctly classified.’
The tree is based on 1,455 observations, half of which are high growth. The first branch of the tree splits on the investment ratio, with a threshold level of 22 percent of GDP. There are 751 observations for which the investment rate is below 22 percent, and the probability of high growth for these observations is 0.36.
His first split thus confirms the findings of prior studies (e.g. Renelt and Levine, Barro, Barro and Lee (1991b)) that high investment is strongly positively correlated with (though not a sufficient condition for) high growth. The finding raises the familiar question whether investment itself should be treated as an endogenous variable. To address this issue, below we report results for a binary tree for investment itself, using the 22 percent threshold to divide investment observations into “high” and “low” subsamples.
Returning to the growth tree, for countries with investment rates below 22 percent of GDP, the next most important discriminant is human capital. Node 2 shows that the 591 observations at or below the ’28th percentile in terms of human capital have a 0.32 probability of being in the high growth group (the probability is for the subsample, and thus conditional on having an investment ratio below 22 percent).
Figure 1: Determinants of high growth: top 1/3 obs vs. bottom 1/3 obs the investment rate exceeds 22 percent of GDP, and for these observations the probability of high growth is almost twice as high, at 0.65.