First we test whether the TR model is statistically significant relative to a linear specification, i.e.
we test the null hypothesis in (4). The values of the Lagrange Multiplier (LM) test are 43.3 and 39.4,
for specifications (5) and (6), respectively. Based on 1000 bootstrap replications, the null hypothesis
in (4) can be decisively rejected regardless of specification (the pvalue for this test is less than 0.01 in
both cases). Subsequently, we subdivide the sample and test for additional threshold levels. For the
subsamples of observations that exceed the threshold level, the LM tests for specifications (5) and (6)
yieldpvalues of 0.35 and 0.43, respectively. Thus, we conclude that no additional threshold levels are
present. In summary, our results provide strong evidence that the inequality–development relationship
is described by a two-regime split of the sample based on percapita income.
Given the presence of only one threshold level in the inequality–development relationship, it is
necessary to estimate it and split the sample accordingly. The estimate of the threshold is $PPP 2199