country club, you are very likely to remain part of this selective group. Only one demotion episode has been recorded for 1950-2008.

How can we evaluate the so-called MIC trap? We can either look at the probability of starting as a middle income country and staying as such, or we can also look at the probability of moving out of that relative income bracket. Alternatively, we can compare the expected mean first passage times, i.e. the expected time to move from one income category to another one (Panel III).<sup>22</sup> From our relative income classification, we could define a lower middle income country as those countries with relative incomes between 0.15 and 0.30, “middle-middle” as 0.30 to 0.45, and upper-middle income country as having an income per capita greater than 0.45 but less than 0.6 of the income per capita of the US.<sup>23</sup> Now that we have a working definition for a middle income country, what does Table 4 tell us about the existence of the MIC trap? First, the probability of being a middle income country and staying as such is lower than the probability of being a low or high income country and remaining in those relative income bracket groups ( _p22_ , _p33_ and _p44_ equal 0.64, 0.40 and 0.53, respectively). Moreover, in fourteen out of forty-eight occasions, “middle-middle” income countries were able to move up to the upper middle income bracket and three transitions from “middle-middle” income to high income were recorded over the period under study. “Middlemiddle” income countries have also been subject to negative shocks and slowdowns in growth, resulting in "downgrades" in their relative income status. However, these backwards transitions were less frequent than the upwards transitions. The lower-middle income group is more problematic – with more persistence – and has only an equally likely chance of moving up or down the ladder.

**Table 5: Ten-year transition matrix 1950-2008**

||[0-1/16) <br>**_Panel I:_**|[1/16-1/8) <br>**_Total numb_**|[1/8-1/4)<br>**_er of transit_**|[1/4-1/2)<br>**_ions_**|≥1/2||[0-1/16) <br>**_Panel II_**|[1/16-1/8) <br>**_I: Mean firs_**|[1/8-1/4)<br>**_t passage t_**|[1/4-1/2)<br>**_ime_**|≥1/2|
|---|---|---|---|---|---|---|---|---|---|---|---|
|[0-1/16)|178|14|0|0|0|[0-1/16)|6.2|37.5|38.3|68.0|113.2|
|[1/16-1/8)|31|86|23|0|0|[1/16-1/8)|71.1|13.2|24.6|54.3|99.5|
|[1/8-1/4)|1|24|94|26|0|[1/8-1/4)|160.9|23.8|23.9|29.7|74.9|
|[1/4-1/2)|0|3|14|67|15|[1/4-1/2)|244.4|103.5|103.7|22.9|45.2|
|≥1/2|0|0|0|1|105|≥1/2|350.4|209.5|209.7|106.0|1.4|
||**_Pan_**|**_el II: Trans_**|**_ition matrix_**|||||||||
|p(i,j)|[0-1/16)|[1/16-1/8)|[1/8-1/4)|[1/4-1/2)|≥1/2|**_Ergodic distri_**|**_bution for t_**|**_ransition m_**|**_atrix_**|||
|[0-1/16)|0.93|0.07|0.00|0.00|0.00||0.16|0.05|0.04|0.04|0.70|
|[1/16-1/8)|0.22|0.61|0.16|0.00|0.00|**_Eigenvalues fo_**|**_r transitio_**|**_n matrix_**||||
|[1/8-1/4)|0.01|0.17|0.65|0.18|0.00||0.41|0.61|0.85|0.99|1.00|
|[1/4-1/2)|0.00|0.03|0.14|0.68|0.15|**_Half-life for tr_**|**_ansition ma_**|**_trix_**||||
|≥1/2|0.00|0.00|0.00|0.01|0.99||50.6|||||

> 22 By definition, the mean first passage time of a diagonal element is zero. For illustrative purposes, the diagonal elements of the matrix in Panel III are comprised of the mean first recurrence time, or in other words, the expected time it takes to move away from a diagonal element and then return to that state for the first time.

> 23 For example, in 2008 (Maddison data), Dominican Republic (0.14), Peru (0.17), Romania (0.16) and Sri Lanka (0.16) are near the 0.15 threshold.   Uruguay (0.32) and Malaysia (0.33) are just above the 0.30 threshold.  Chile

> (0.42) and Latvia (0.48) are near the 0.45 threshold.  Estonia (0.64) and South Korea (0.63) are just over the 0.60 threshold.

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