||Table 5: Empi<br>Depen<br>|rical results fo<br>dent Variable<br>|r logit mod<br>: PPP<br>|el<br>|||
|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|(6)|
|IRA|‐2.56E‐17|0.0019|‐0.3003|‐0.4825|‐3.2418**|‐2.5139*|
||(0.4798)|(0.5296)|(0.5154)|(0.5933)|(1.3472)|(1.4044)|
|GDP per capita||0.0001***||0.0002***||0.0001**|
|||(0.00005)||(0.00005)||(0.00005)|
|Inflation|||0.0796*|0.1133**|0.1473**|0.1617**|
||||(0.0418)|(0.0521)|(0.0651)|(0.0690)|
|2.Europe and C. Asia and IRA|||||2.8261*|1.7713|
||||||(1.4684)|(1.1375)|
|3.Lat. Am. And Carib. and IRA.|||||3.7601***<br>(1.4181)|2.5250*<br>(1.5264)|
|4.Mid. East and N. Africa, and IRA.|||||3.0673|2.5494|
||||||(2.0422)|(2.2595)|
|Constant|‐0.1719|‐1.5873***|‐0.2563|‐1.8891***|‐0.3636|‐1.6562**|
||(0.3393)|(0.5700)|(0.3509)|(0.6148)|(0.3746)|(0.6610)|
|Observations|70|70|70|70|68|68|
|������ �<sup>�</sup>|0|0.1372|0.0522|0.2127|0.1873|0.2621|
|Log Likelihood<br>|‐48.26|‐41.64|‐45.74|‐37.99|‐37.92|‐34.43|
|LR�<sup>�</sup><br>|0|13.24|5.04|20.53|17.48|24.46|
|Prob <�<sup>�</sup>|1|0.0013|0.0804|0.0001|0.0037|0.0004|

Standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1 South Asia is dropped as all observations lack and autonomous regulator; East Asia is dropped as all 6 observations have PPP; sub‐Saharan Africa is omitted variable The goodness‐of‐fit results show that the pseudo R<sup>2</sup> increases when controlling for income per capita and for regional interaction terms and the model reaches a relatively good fit (considered to be between 0.2 and 0.4 according to McFadden (1998)). This better fit is also seen in the log‐likelihood, which is maximized when controlling for all variables (i.e. model 6). Finally, the probability of obtaining the χ^2 statistic if there is no effect of the independent variables (Prob < χ^2) is lowest when controlling all variables as well (model 6).

The interpretation of the table is somewhat subtle, since the coefficients reported on each independent variable need to be transformed into the odds of having PPP depending on the value taken by the independent variables. A negative coefficient implies that the odds ratio will be smaller than 1. When this ratio is less than 1, it means the odds of having PPP (i.e. PPP=1) when there is an IRA (i.e. IRA=1) are actually lower than when there is no IRA (i.e. IRA=0). If the odds ratio is above 1, the odds of having PPP when there is an IRA are higher than the odds of having PPP without a regulator. The specific measure of these odds is obtained by exponentiation of the coefficient on the IRA.

If models (5) and (6) respectively are considered to be the most complete, the odds that a country with an autonomous regulator has private participation in the water and sanitation sector are between exp<sup>(‐3.2418)</sup> = 0.04 and exp<sup>(‐2.5139)</sup> =0.08 times higher than a country without a regulator. The impact is however stronger in Latin America; more precisely, the odds that a Latin American country with a regulator has private financing in the water sector are exp<sup>(‐3.2418+3.7601)</sup> = 1.68 times higher than a Latin American country lacking such a regulator. In terms of Europe and Central Asia, where the results are only slightly significant and the impact only appears when income per capita is not controlled for, the odds that a European or Central Asian country has PPP are exp<sup>(‐3.2418+2.8261)</sup> =0.66 times higher when the country has a regulator than when it does not. Note that in the Middle East, 9