several years prior to the dependent variables. The strongest results are found using _WVS_ , from surveys conducted mostly in 1995 and 1996, more than a decade prior to the SMPD, when use of country PFM systems and direct budget support were much less prevalent for donors in general.

To this point, we have included donor and/or recipient fixed effects in all of our tests. This method most effectively captures the influence of otherwise unmeasured determinants of use of country systems. Depending on the specification, however, Hausman tests do not always indicate fixed effects are preferred over random effects. In such cases, it is common to use random effects instead of fixed effects, on efficiency grounds. We therefore present random effects results for _PFM_ , _DBS_ and _PBA_ in equations 1-3 (respectively) of Table 10. Donor and recipient characteristics can be included together in these tests. However, we do not include the public opinion variables from Table 9, because they cut the sample size by half or more.

Most results obtained using fixed effects tests change very little in the random effects tests. Coefficients for _donor aid share_ are somewhat smaller using random effects, for _PFM_ and _PBA_ (equations 1 and 3 in Table 10), but not for _DBS_ (equation 2). Results for _HIPC completion_ , _aid/GNP_ , and the three CPIA variables change very little in most cases. One exception is that _Transparency_ is highly significant in the _PBA_ regression in Table 10; the corresponding t-stat using fixed effects was only 1.52 (equation 2 of Table 7). The only notable change in results for the donor groupings dummies is for the _non-MDBs_ : their coefficients in _DBS_ and _PBA_ random effects regressions (Table 10, equations 2 and 3) remain positive, but are smaller in magnitude. When recipient fixed effects were included (Table 8, equation 3), _PBA_ was significantly higher for the _non-MDBs_ than for the omitted category of _other DAC bilaterals_ but in random effects the difference is smaller and not significant.

Equations 4-6 in Table 10 report random effects tobit models for each of the three dependent variables, which are bounded by 0% and 100%.<sup>31</sup> For example, of the 782 observations in equation 1, _PFM_ equals 0% for 203 cases and 100% for 37 others. All results significant at conventional levels in equations 1-3 remain significant in their respective counterparts using tobit in equations 4-6, and no coefficients change sign.<sup>32</sup> For space reasons we do not report a table of results for random effects versions of the Table 9 (fixed effects) tests showing public support for aid increases trust in country systems.

> 31 Fixed-effects tobit estimates are biased, so we report tobit results only for random effects models.  The value added of tobit estimation is relatively small (Angrist and Pischke, 2009), so we report tobit results only to show our main results from linear (fixed and random effects) regressions are robust to the most obvious nonlinear alternative. 32 Coefficient magnitudes are not directly comparable between random effects and random effects tobit: in tobit, a coefficient measure the marginal effects of a one-unit change in a regressor, evaluated at the means of the other regressors, on the latent (unobserved) dependent variable.

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