Does Public Spending on Tertiary Education Increase Tertiary Enrollment? Evidence from a Large Panel of Countries

2.1 Framework

To provide a framework for our theoretical discussion of the impact of public tertiary education spending on tertiary enrollment and for our empirical model, including our review of the empirical literature (in the next section), we start with a simple identity that relates total tertiary enrollments, E, to public expenditures on tertiary education, P, and to the public costs per tertiary student, C:

By dividing both sides of the equation by the number of persons of tertiary education age (defined as 18–24 years) and multiplying the right-hand side of the equation by G D P G D P , and considering that GDP is the product of GDP per capita and population, we obtain an equation that relates the gross enrollment rate in tertiary education (i.e. the number of people enrolled in tertiary education as a fraction of the total number of people aged 18 to 24), GERT, to public expenditures on tertiary education as a proportion of GDP, EDUXT, the public costs per student as a proportion of GDP per capita, COSTS, and the proportion of the population of tertiary education age, TERTPOP:

The logarithmic form of this equation is:

2.2 Theoretical Discussion

Although equations (2) and (3) represent an identity, they can be given an economic interpretation. The supply-side interpretation regarding EDUXT is as follows: An increase in the proportion of GDP allocated to tertiary education in the form of direct expenditures, such as salaries for professors and other teachers, or spending on the construction of university buildings and the purchase of textbooks and scientific journals, results in an increase in the supply of tertiary education, provided that the proportion of the population of tertiary education age and the relative costs per student enrolled remain unchanged (or increase less rapidly).

A demand-side interpretation of the identity given by equations (2) and (3) regarding EDUXT is that an increase in public expenditure on tertiary education in the form of indirect expenditures, such as public subsidies to students for scholarships and other grants, as a proportion of GDP, raises the demand for tertiary education and thus increases the tertiary enrollment rate, provided that TERTPOP and COSTS do not rise (or increase less rapidly) and the supply of tertiary education is not fully inelastic.

Regarding TERTPOP, it can be argued that an increase in the proportion of the population of tertiary education age implies that scarce education resources must be spread over a larger number of students, assuming that the demand for education increases with the population of tertiary education age. This increase in per capita costs reduces the supply of tertiary education per person of tertiary education age and, consequently, the tertiary enrollment rate.

Similarly, an increase in COSTS implies a shift of the supply curve to the left and thus a reduction in enrollment (for constant tertiary education expenditures). The simple logic is that as more funds are directed to cover the increased costs per student, less money is available for expanding access, providing scholarships, or supporting additional students. Alternatively, higher costs can make tertiary education less accessible if these costs are passed on to students through higher tuition fees. However, an increase in costs per student (as a proportion of GDP per capita) may also reflect an increase in the quality of education (better facilities, more qualified teaching personnel, advanced materials). This quality improvement could positively affect enrollment, even if the increased costs are partly passed on to the students (through higher tuition fees), if potential students perceive the increased quality as beneficial for their studies and future careers. Thus, the elasticity of GERT with respect to COSTS does not necessarily need to be negative or equal to one.

While equation (3) assumes that the elasticities of GERT with respect to EDUXT, TERTPOP, and COSTS are equal to one (in absolute value), it is useful for further discussion to consider the following more general version of equation (3):

Our primary interest is in the elasticity of GERT with respect to EDUXT, α. This elasticity may be smaller than one or even zero for several reasons.

First, in addition to public education expenditures, there are private education expenditures, such as tuition fees, that finance higher education to some extent. Thus, individuals might reduce their education expenditures when higher education is financed by the government. In other words, public spending could merely act as a substitute for private spending. Second, a large part of government expenditures on tertiary education consists of salaries for professors and other academic staff. If the supply of academics is relatively constant, an increase in public funds for tertiary education may merely lead to higher salaries rather than an increase in the number of academics employed. Third, public funds for tertiary education might not be used effectively, for example, if a significant portion is consumed by administrative overheads rather than directly benefiting students, or if funding priorities are imbalanced, favoring research over teaching, scholarships, grants, and student support services. Additionally, funding decisions may be driven by political considerations rather than actual educational needs. Fourth, if there is already a high level of tertiary education enrollment, additional funding may yield diminishing returns. Once the majority of the population willing and able to pursue higher education is enrolled, further expenditures may not significantly increase enrollment rates. Fifth, many prospective students face challenges such as inadequate academic preparedness, cultural and social constraints, and family responsibilities, which financial aid alone cannot overcome. These barriers can deter students from pursuing higher education even when financial support is available. Sixth, if the public perceives that a tertiary education degree does not significantly enhance job prospects or earning potential, they may be less motivated to enroll, irrespective of increased funding. This perception can be influenced by labor market conditions and the visibility of successful career paths that do not require a tertiary degree.

Finally, we note that the third point might explain why the impact of public tertiary education spending on tertiary enrollment might be larger in country groups with higher income than in country groups with lower income, where public funds for tertiary education may not be used efficiently to expand access to higher education. In contrast, the fourth point could explain why public tertiary education spending might have a larger effect on the tertiary enrollment rate in less developed countries, where fewer people are enrolled than in more developed countries.

2.3 Baseline Empirical Model, Data, and Estimation Issues

To estimate the elasticity of GERT with respect to EDUXT, we employ the following model:

where i and t are country and time indices; and X _it is a vector of control variables. In our baseline specification, we not only control for logTERTPOP _it and logCOSTS _it , but we also include the log of real GDP per capita, logGDPPC _it , the log of the urbanization rate, logURBAN _it , and the log of the gross enrollment rate in secondary education, logGERS _it , as control variables, based on the previous literature (which we will discuss in Section 3). In addition, we control for unobserved time-invariant country characteristics (such as geography and culture), μ _i , by including country dummies, as well as time-varying unobserved common factors (such as global business cycles or global crises), f _t , by including time dummies.

Regarding logCOSTS _it as a control variable, we explicitly note that an increase in public education cost per student may prompt governments to allocate a higher proportion of their GDP to public education expenditures to support accessibility and affordability. Thus, logCOSTS _it may have a positive effect on logEDUXT _it . Given that an increase in the public costs per student as a proportion of GDP per capita may also affect the tertiary school enrollment rate, the omission of logCOSTS _it as a covariate in an empirical model of the impact of public tertiary education spending on tertiary enrollment may result in a classical omitted variable bias. In this case, the estimated elasticity of public tertiary education spending on tertiary enrollment would capture not only the true effect of logEDUXT _it on logGERT _it but also the effect of education costs per student on the tertiary enrollment rate. Thus, the omission of logCOSTS _it may result in a downwardly biased estimate of α if these costs have a negative effect on the tertiary enrollment rate and a positive effect on public expenditures on tertiary education as a proportion of GDP. To avoid this bias, it is important to control for logCOSTS _it .

However, if there are factors that limit the positive impact of public spending on tertiary education enrollment, as discussed above, an increase in logEDUXT _it results in higher per-student public tertiary education expenditures or in logCOSTS _it . In other words, to the extent that public tertiary education spending (as a proportion of GDP) is not fully effective, it is accompanied by an increase in public tertiary education expenditures per student (as a proportion of GDP per capita) and hence in public costs per student (as a proportion of GDP per capita). Therefore, one might be concerned that including logCOSTS _it as a covariate might introduce an ‘included variable bias’. In this scenario, the estimated elasticity α does not fully capture the effect of logEDUXT _it on logGERT _it if public costs or expenditures per student increase due to the limited effectiveness of public expenditures. To address this concern, we also present estimation results from several specifications that exclude logCOSTS _it .

As our measure of COSTS _it , we use public tertiary education expenditures per student as a percentage of GDP per capita, consistent with several other studies that also utilize public education expenditure per student as a percentage of GDP or GNP per capita to measure the unit costs of education relative to GDP or GNP per capita (see, e.g. Appiah and McMahon 2002; Colclough and Al-Samarrai 2000; Keller 2006).

The definition of the variables and the sources used are presented in Table A1 in the appendix. We include all available data from these sources, resulting in an unbalanced panel of 149 countries with data between 1997 and 2018. The countries included in our sample are listed in Table A2 in the appendix. Summary statistics are presented in Table A3.

We estimate equation (5) using the OLS fixed effects (FE) estimator as the baseline estimator. Given our relatively long sample period of 22 years, there is a concern that this estimator might provide invalid inference that can be spurious when the underlying variables are non-stationary. Monte Carlo simulations by Entorf (1997) and Kao (1999) demonstrate that there is a risk of spurious regressions in fixed effects regressions with non-stationary variables, even with 10 time series observations per country. They also demonstrate that an increase in the time-series dimension (T) increases this risk, and that an increase in the number of cross-sectional units (N) does not decrease the risk of spuriously indicating a relationship but may even increase it. Since our panel is highly unbalanced, characterized by numerous data gaps and only a few countries having more than 10 consecutive time series observations, with none having a complete time series over the entire observation period, the risk of spurious regressions due to non-stationary data in panels with a large time series dimension should be small in our study. However, there is still a risk. To eliminate the danger of spurious regressions, we artificially reduce the time series dimension of our panel by using three-year averages, except for the period 2015–2018, which is represented by a four-year average.^[1] Consequently, our panel consists of seven periods: 1997–1999, 2000–2002, 2003–2005, 2006–2008, 2009–2011, 2012–2014, and 2015–2018. Using n-year averages is a common practice in panel studies to capture long-run effects and to smooth business-cycle fluctuations. In the empirical analysis, we utilize 5-year averages as well as annual data as robustness checks.^[2]

Another concern is that the effect of public tertiary education spending on tertiary enrollment might differ across countries with different income levels, as noted above and suggested by some studies (discussed in the next section). To address this concern, we also present results for different income groups: low-income countries (LIC), lower-middle-income countries (LMIC), upper-middle-income countries (UMIC), and high-income countries (HIC).^[3]

A further concern is the potential endogeneity of public expenditures on tertiary education as a proportion of GDP: An increase in the tertiary enrollment rate may reflect a higher demand for higher education. When governments respond to the increased enrollment rate by allocating more resources to tertiary education, the estimate of α may overstate the positive causal effect of public tertiary education spending on tertiary enrollment. Alternatively, it could be that an increase in the tertiary enrollment rate leads to an increase in human capital, and thereby an increase in GDP and thus a decrease in public expenditures on tertiary education as a proportion of GDP. In this case, the estimate of α may understate the elasticity of GERT _it with respect to EDUXT _it .

To address the potential endogeneity of logEDUXT _it , we also estimate specifications with lagged values of all regressors. Additionally, we employ the system GMM estimator developed by Arellano and Bover (1995) and Blundell and Bond (1998). As is well known, this estimator (designed for small-T large-N panels such as the one used here) is a dynamic panel estimator that accounts for endogeneity using internal instruments while avoiding the well-known ‘Nickell bias’, which arises from applying a fixed effects estimator to a lagged dependent variable model in a panel with small T.^[4] To demonstrate the robustness of our results, we estimate two GMM models: one that treats only public tertiary expenditures as endogenous, and another that treats all explanatory variables (including lnCOSTS _it ) as endogenous.^[5]

3.1 Preliminary Remarks

Before discussing the existing evidence in more detail, it is noteworthy that two studies – those by Bergh and Fink (2006, 2008) – use cross-sectional data and thus employ cross-sectional analysis, which is known to inherently suffer from omitted variable bias due to unobserved country-specific time-invariant factors. The remaining six studies – those by Winter-Ebmer and Wirz (2002), Yang and McCall (2014), Buckner and Khoramshahi (2021), Yang and St. John (2023), Hajebi et al. (2023), and Wang, Wang, and Zong (2023) – employ panel data models, which allow control for country-specific time-invariant factors.

In addition, it is worth mentioning that the samples used in these studies vary widely in terms of the number of countries included. Three studies use relatively small samples, with between 14 and 18 countries (Hajebi et al. 2023; Wang, Wang, and Zong 2023; Winter-Ebmer and Wirz 2002). Three are based on samples of medium size, with a maximum number of countries between 64 and 86 (Bergh and Fink 2008; Yang and McCall 2014; Yang and St. John 2023), and two on relatively large samples, with a maximum number of countries between 122 and 127 (Bergh and Fink 2006; Buckner and Khoramshahi 2021).

Moreover, the observation periods vary across the studies. One study, by Bergh and Fink (2006), considers only one year. The observation period of another study, by Hajebi et al. (2023), includes only 10 years. The majority of studies are based on periods of medium length, between 12 and 22 years (Buckner and Khoramshahi 2021; Wang, Wang, and Zong 2023; Winter-Ebmer and Wirz 2002; Yang and McCall 2014; Yang and St. John 2023). One study, by Bergh and Fink (2008), considers a relatively long sample period of 31 years. However, this study is purely cross-sectional.

3.2 Main Results

The individual results of existing studies on the impact of public tertiary education spending on tertiary enrollment can be summarized as follows.

Only three studies – those by Buckner and Khoramshahi (2021), Hajebi et al. (2023), and Wang, Wang, and Zong (2023) – report statistically significant positive coefficients on their tertiary expenditure variable. However, Hajebi et al. (2023) present the results of only one regression, while Buckner and Khoramshahi (2021) and Wang, Wang, and Zong (2023) present the results of several regressions, where the coefficients are sometimes insignificant. Surprisingly, Wang, Wang, and Zong (2023) find a positive coefficient in their total sample consisting of both developed and developing countries. However, when the sample is subdivided into developed and developing countries, the coefficient from the GMM estimator becomes negative and insignificant in both subsamples. In one study – that by Winter-Ebmer and Wirz (2002) – the coefficients are always insignificant. Two studies – those by Bergh and Fink (2006, 2008) – find both statistically significant negative coefficients and statistically insignificant coefficients. Finally, the coefficients on the public tertiary expenditure variable are consistently negative and statistically significant in two studies – Yang and McCall (2014) and Yang and St. John (2023). It is worth mentioning that Yang and McCall (2014) find a larger negative coefficient (in absolute value) for developed countries than for developing ones. Overall, the results are mixed and sometimes conflicting, with no robust evidence supporting a positive effect of public tertiary education spending on tertiary enrollment.^[6]

3.3 Dependent Variables and the Tertiary Expenditure Variables

All studies use the gross tertiary enrollment rate as the dependent variable or the change in the gross tertiary enrollment rate. The only exception is Yang and St. John (2023), who use absolute enrollments in short-cycle tertiary education. To provide one explanation for the mixed results, we now discuss the tertiary expenditure variables used in these earlier studies.

While one study (Winter-Ebmer and Wirz 2002) uses public tertiary education expenditures in absolute terms as the explanatory variable, three studies (Buckner and Khoramshahi 2021; Hajebi et al. 2023; Wang, Wang, and Zong 2023) use public tertiary education expenditures as a percentage of GDP, similar to our study. Four studies employ public tertiary education expenditures per tertiary student, either in absolute terms (Yang and McCall 2014) or as a percentage of GDP per capita (Bergh and Fink 2006; 2008; Yang and St. John 2023). All these latter four studies report negative, although not necessarily significant, coefficients. However, as discussed in Section 2, other studies use public education expenditures per student (as a percentage of GDP per capita) as a measure of public costs per student. Thus, the results of these four studies are very likely to reflect the effect of public costs per student on tertiary enrollment, rather than the effect of public education expenditures on tertiary enrollment.

Another, complementary explanation for the significant negative coefficients on public education expenditures per student (as a percentage of GDP per capita) is, of course, their likely endogeneity, given that the number of students implicitly appears in both the tertiary school enrollment rate and public education expenditures per student (as a percentage of GDP per capita).

Interestingly, all studies that report positive (but not necessarily significant) coefficients use public education expenditures (as a percentage of GDP) as a regressor. Admittedly, in two of these studies (Wang, Wang, and Zong 2023; Winter-Ebmer and Wirz 2002), the coefficient on this variable is also negative (but insignificant) in some regressions.^[7]

3.4 Weaknesses of Previous Studies

We now briefly discuss the weaknesses of previous studies. As noted above, four out of the eight existing studies on the impact of public tertiary education spending on tertiary enrollment use public tertiary education expenditures per student as their measure of public tertiary expenditures. Therefore, they are very likely to capture, at least to some extent, the impact of public costs per student on tertiary enrollment rather than the effect of public education expenditures on tertiary enrollment.

The remaining four studies use public education expenditures (as a percentage of GDP) as a regressor. However, these studies do not control for public costs per student as a proportion of GDP per capita. It is clear, therefore, that their estimates may suffer from an omitted variable bias, as discussed in Section 2.3.

In addition, six out of the eight studies (Bergh and Fink 2008; Buckner and Khoramshahi 2021; Hajebi et al. 2023; Wang, Wang, and Zong 2023; Yang and McCall 2014; Yang and St. John 2023) do not address the potential endogeneity of their measure of public tertiary education spending.^[8] Thus, it cannot be ruled out that the results of these studies are biased by endogeneity.

Two studies – those by Winter-Ebmer and Wirz (2002) and Bergh and Fink (2006) – use an instrumental variable (IV) approach, in addition to OLS, to address potential endogeneity problems. However, even the results of these studies can be biased if the instruments are weak (i.e. not sufficiently correlated with the potentially endogenous variable) and/or invalid (i.e. correlated with the error term and hence with the dependent variable).^[9] As is well known, it is difficult, and sometimes impossible, to find external variables that qualify as strong and valid instruments in macro studies.

Moreover, the existing panel studies use annual observations and include countries with at least 10 time-series observations. Therefore, it cannot be ruled out that some of their significant results reflect spurious correlations caused by non-stationary data, as discussed in Section 2.3.

Finally, three studies – those by Buckner and Khoramshahi (2021), Hajebi et al. (2023), and Wang, Wang, and Zong (2023) – that employ panel data techniques do not control for time-varying unobserved common factors (such as global business cycles or global crises) that may influence both the tertiary school enrollment rate and public tertiary education expenditures. Thus, the estimates from these studies may be additionally biased.

In summary, all existing studies suffer from several methodological shortcomings. In the following analysis, we address these shortcomings and use a larger sample of countries than any previous study, as well as a longer sample period than the existing panel studies.

4.1 Baseline Fixed Effects Results

Column 1 in Table 2 presents the results from our baseline model, based on three-year averages. The coefficients of the control variables are as theoretically expected. However, while the coefficients on logCOSTS _it , logTERTPOP _it , and logGDPPC _it are significant at least at the 10 % level, those on logURBAN _it and logGERS _it are not significantly different from zero.

The insignificance of the gross secondary school enrollment rate is consistent with the findings of Bergh and Fink (2008) and Yang and St. John (2023). Other studies, however, find significant positive coefficients for the secondary school enrollment rate (see, e.g. Wang, Wang, and Zong 2023; Yang and McCall 2014), as we do in some of the regressions below. Moreover, the insignificance of the urbanization rate is consistent with the findings of Bergh and Fink (2008) and Buckner and Khoramshahi (2021). The significant positive coefficient on GDP per capita accords with the findings of Bergh and Fink (2006), Yang and McCall (2014), Buckner and Khoramshahi (2021), and Wang, Wang, and Zong (2023), but contrasts with the results of Bergh and Fink (2008) and Yang and St. John (2023), who report insignificant coefficients. Furthermore, the significant negative coefficient on logTERTPOP _it is in line with the results of Bergh and Fink (2006) and Yang and McCall (2014), whose findings suggest that changes in the population structure toward a higher (lower) share of the population of tertiary education age are negatively (positively) correlated with the tertiary enrollment rate. Finally, consistent with most findings of those studies that examine public tertiary education expenditures per student (discussed in the previous section), the coefficient on logCOSTS _it is negative and statistically significant.

Turning to our variable of interest, the results reveal a positive and significant coefficient on logEDUXT _it . According to the point estimate, a one percent increase in public expenditures on tertiary education as a proportion of GDP leads to a 0.829 percent increase in the gross enrollment rate in tertiary education. In terms of economic significance, this estimate implies that a one-standard-deviation increase in logEDUXT _it is associated with a 46.78 percent increase in the standard deviation of the enrollment variable (0.829 × 0.6312441/1.118629),^[10] indicating an economically significant effect.

4.2 Robustness Checks

In column 2 of Table 2, we investigate whether the significant positive coefficient on logEDUXT _it is driven by potential outliers (or extreme values) by winsorizing our dependent variable and our public expenditure variable at the one percentile level in both tails of the distribution. While the coefficient is slightly smaller than that in Column 1, it remains highly significant, suggesting that the significant positive coefficient on logEDUXT _it is not driven by potential outliers. However, since winsorizing replaces extreme values with less extreme values, it can introduce inaccuracies in data where extreme values represent legitimate values. Therefore, we proceed with the unwinsorized data.

In columns 3 and 4, we check the robustness of our results to the use of annual data and five-year averaged data, respectively. The coefficient on logEDUXT _it remains positive and significant at the 1 % level.

In Table 3, we test whether our results are driven by a particular income group by estimating equation (5) for low-income countries, lower-middle-income countries, upper-middle-income countries, and high-income countries. While the coefficient on logEDUXT _it is highest for upper-middle-income countries and lowest for low-income countries, the differences in the estimated coefficient across these country groups are not very large, and the coefficient remains statistically highly significant for all country groups.

A possible explanation for the finding that the estimated elasticity is lowest in low-income countries is that these countries, as a group, relatively inefficiently use public funds for tertiary education to expand access to education, as discussed under point three in Section 2.2. Similarly, the smaller coefficient on logEDUXT _it for lower-middle-income countries compared to upper-middle-income countries may be explained by the more efficient use of public funds for tertiary education in the latter group. In contrast, the relatively high level of tertiary education enrollment in high-income countries and diminishing returns may explain why the estimated coefficient on logEDUXT _it is higher in upper-middle-income countries than in high-income countries, as discussed under point four in Section 2.2.

In Table 4, we address the potential endogeneity of logEDUX _it . Column 1 presents the results with lagged variables. The coefficient on logEDUX _it becomes somewhat smaller but is still significant at the 1 % level.

In columns 2 and 3 of Table 4, the GMM results are reported. In column 2, only logEDUX _it is treated as endogenous, whereas the other explanatory variables are predetermined. In column 3, all explanatory variables are treated as endogenous.

While it is perhaps needless to say that the lagged dependent variable is always treated as predetermined, it is important to say that we use the two-step estimator as it is more efficient than the one-step estimator. However, a well-known property of the two-step estimator is that the standard errors may be severely biased downwards in small samples. To address this problem, we adopt the finite sample correction to the standard errors proposed by Windmeijer (2005).

Moreover, it is well known that GMM can exhibit the problem of ‘too many instruments’ when the number of instruments exceeds the number of cross-sectional units. The proliferation of instruments can lead to unreliable inference and weaken the Hansen-J test of overidentifying restrictions. To avoid this problem, we use only the second and third lags of the regressors as instruments and collapse the instrument matrix.

Following common practice, we also report the p-values of the Arellano and Bond (1991) test for second-order serial correlation (AR2), the p-values of the Hansen-J test of overidentifying restrictions (Hansen), and the number of instruments. The AR2 test indicates that the errors exhibit no second-order serial correlation, the Hansen test does not reject the validity of the instruments, and the number of instruments is always less than the number of cross-sectional units. We thus conclude that the models presented in columns 2 and 3 are correctly specified.

As before, the coefficient on logEDUXT _it is positive and statistically significant in columns 2 and 3. While the estimated coefficient on logEDUXT _it represents short-run effects, the long-run effects can be calculated by dividing the estimated short-run coefficients by one minus the coefficients on the lagged dependent variable. Thus, the estimates in column 2 imply a long-run elasticity of 0.993, and those in column 3 imply a long-run elasticity of 0.957. The former implies that, in the long run, a one-standard-deviation increase in logEDUXT _it is associated with a 56.04 percent increase in the standard deviation of logGERT _it , and the latter implies a 54.00 percent increase in the standard deviation of logGERT _it as a result of a one-standard-deviation increase in logEDUXT _it . These values are greater than, but still close to, the estimated magnitude (46.78 percent) implied by the coefficient in column 1 of Table 2.

A concern with the above results could be that they suffer from an ‘included variable bias’, where the estimated elasticities do not capture the effect of public tertiary education spending on the tertiary enrollment rate when ineffective public tertiary education expenditures increase the public costs or expenditures per student (as a proportion of GDP per capita). To address this concern, and to ensure that our results suffer neither from an omitted variables bias nor from an included variable bias, we reestimate our main models excluding logCOSTS _it as a control. The results from this robustness check are reported in Table 5.

The estimated coefficients on logEDUXT _it are still positive and highly significant. As expected, the estimated elasticities and their economic magnitudes are smaller than those in Tables 1 and 3. However, while the differences between the estimated coefficients on logEDUXT _it in columns 1 and 2 of Table 5 (0.100 and 0.158, respectively), and those in column 1 of Table 2 (0.829) and column 1 of Table 4 (0.547), are very large in relative terms, the discrepancies in the estimated long-run elasticities implied by the results from columns 1 and 2 of Table 5 – 0.767 (0.283/(1–0.631)) and 0.603 (0.284/(1–0.529)) – and the estimated long-run elasticities implied by the results from columns 2 and 3 of Table 4 – 0.993 and 0.957, respectively – are moderate.

It is perhaps interesting to note that the estimated elasticities for public tertiary education spending in the regressions that do not control for endogeneity (in column 1 of Table 2 and in column 1 of Table 5) are smaller than the long-run elasticities for public tertiary education spending from the GMM regressions (in Tables 3 and 4), which do control for endogeneity. This difference might suggest that not controlling for endogeneity induces a downward bias in the estimated coefficient on logEDUXT _it .

Finally, we note that all our estimated coefficients on logEDUXT _it , including the long-run estimates, are smaller than one. This is consistent with our theoretical discussion in Sections 2.1 and 2.2, according to which nothing suggests that the elasticity of GERT _it with respect to EDUXT _it is greater than one (or negative), and strengthens our confidence in our results.