A variant of Spence’s analysis has been developed by Felipe et al. (2012a). They identify two middle-income bands: one with a range of $2,000 to $7,500, and the other with a range of $7,500 to $11,500 [1990 PPPs]. If a country stays in the first range for longer than 28 years or longer than 14 years in the second range, it is classified as stuck in a middle-income trap. Felipe et al. identify 35 middle-income countries that are stuck, out of a sample of 52 countries that they looked at.

The bands of income levels set by Spence and Felipe of where middle-income countries could potentially become trapped are heuristic. Others have taken an econometric approach. Eichengreen et al. (2013) ask whether middle-income countries are more likely than others to experience a growth slowdown, defined as a decline of at least 2 percentage points relative to a 7-year moving average.<sup>8</sup> They conclude that there appear to be two ranges of growth slowdowns: one between $10,000 and $11,000 and the other between $15,000 and $16,000. The implication is that countries may find themselves slowing down at lower income levels than previously believed and decelerate in steps, rather than smoothly or at a single point in time. They also emphasize the importance of moving up the technology ladder in order to avoid such a secular slowdown.

Aiyar et al. (2013) take a similar approach, differing from Eichengreen in the counterfactual against which a growth slowdown is measured. Aiyar et al. use the predictions of a Solow growth model. They identify and examine 123 episodes of growth slowdowns since 1960 and find that indeed middle-income countries (defined as those with income levels between $1,000 and $12,000) have a greater frequency of slowdowns than either advanced or low-income countries.<sup>9</sup> They also find that some of the explanatory variables for growth slowdowns differ between middle-income countries and the full sample; middle-income countries with low levels of infrastructure and limited regional integration are more likely to have slowdowns. This evidence is consistent with the authors’ prior belief that in practice anxiety over growth slowdowns has been particularly acute in middle-income countries.

A third definition of the middle-income trap is based on the absence of convergence to a benchmark advanced country, typically the United States. Im and Rosenblatt (2013) is a good example. They create a set of thresholds based on a country’s GDP per capita relative to that of the United States, and look at the probability of a country transitioning to a higher category. They find that the probability of countries with middle-incomes transitioning to a higher category is quite low; in other words, evidence of a middle-income trap where convergence with the US stops.

This same conclusion is reached by Agenor and Canuto (2012). They plot GDP per capita relative to the United States in 1960 against the same relative income measure in 2008. Updating this analysis, Figure 4 below shows that most middle-income countries are indeed stuck; they are either

> 8 Eichengreen et al. also limit the sample to those countries that had growth rates higher than 3.5 percent per annum, and whose income levels exceeded $10,000 in PPP terms.

> 9 A growth slowdown is defined as occurring by looking at the residual of actual growth less predicted growth. When this difference is less than the 20<sup>th</sup> percentile of the difference in residuals over all countries and all time periods (and continues for two continuous periods), then there is a growth slowdown.

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