In the models entitled Outliers, we re-estimate our preferred model (IV in table 2) after
dropping all observations for which a Grubbs test suggest that they are an outlier.12 We use
a signicance level of 95% in the models for secondary and tertiary education expenditures.
This reduces the number of observations in the model for tertiary education expenditures by a
large amount, and in the model for secondary education expenditures somewhat moderately.
In the model with primary education expenditures, however, no observations are regared as
outliers at a signicance level of 95%. We therefore reduce the signicance level sucessively
for primary education expenditures. But even at a signicance level of 50 %, only two
observations are considered as outliers for this type of expenditures, which suggests that
most countries spend similar per capita amounts (scaled by their respective GDP per capita)
for primary education.
In the models entitled Budget, we use the alternative measure for public spending on the
three types of educational programs. The dependent variables in these models are the bud-
get shares. Since the budget shares are constrained to be between 0 and 100, using them
as dependent variables violates the assumptions for OLS to be appropriate. We therefore
transform the dependent variables by applying the logistic function before conducting the
estimations.
Since the number of students in the three educational programs do not appear at the
left-hand side in the Budget models, we have to adapt the right hand-side of equation 10
by explicitly including both the population shares of the relevant age groups and the gross
enrollment rates. This is necessary because the “demand” for a particular type of educational
spending will increase with the number of student and their enrollment rates.
In the models entitled Aid, we additionally include into the baseline model the amount
of development aid divided by GDP as an additional control variable. The rational for in-
cluding this variable is that donor countries may insist that developing countries use aid for
certain types of educational programs. According to Bloom et al. (2006), for example, inter-
national donor agencies have generally emphasized lower and deemphasized higher education
in developing countries.13
As in the baseline models, we need to instrument total education expenditures per student
in the Outliers and Aid models. We do that by using the same instruments as in the baseline
models. In the Budget models, we do not use instruments and thus report the simple xed
eects estimates. All models include year xed eects and use robust standard errors for
hypothesis tests.
The results for this set of robustness checks are collected in table 4. They largely conrm
the baseline results. The interaction eect is generally positive in the primary and negative
12The Grubbs test has been implemented by Couderc (2007) in Stata.
13Note that our original data for the aid variable had missing observations for “wealthy” countries. We
replaced these missing observations with 0 to ensure that we can include these countries in the regressions.
Note furthermore that several developing countries in our sample had a negative value for the development aid
variable in some years. We replaced these values with 0, too.
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