In this paper, we test whether the growth experience of a sample of OECD countries over the past three decades is more consistent with the human-capital augmented Solow model of exogenous growth, or with an endogenous growth model à la Uzawa-Lucas with constant returns to scale to “broad” (human and physical) capital. We exploit the different non-linear restrictions implied by these two models to discriminate between them. Using pooled crosscountry time-series data, we specify our growth regression by imposing cross-country homogeneity restrictions only on long-run coefficients, while letting the speed of convergence and short term dynamics to vary across countries. While there are indeed good reasons to believe in common long-run coefficients, given that OECD countries have access to common technologies and have intensive intra-industry trade and foreign direct investment, the theoretical models imply that the speed of convergence to the steady state differs across countries because of cross-country heterogeneity in population growth, technical change and progressiveness of the income tax. Therefore, standard dynamic fixed effect specifications, by imposing cross-country homogeneity restrictions on speed of convergence and short-run parameters, suffer from a heterogeneity bias and are not suited to implement our tests. The results suggest a strong effect of human capital accumulation: the estimated long-run effect on output of one additional year of education (about 6-9%) is also within the range of the estimates obtained in microeconomic analyses of the private returns to schooling. Our estimated speed of convergence is too fast to be compatible with the augmented Solow model, while is consistent with the Uzawa-Lucas model with constant returns to scale. This main finding is robust to several robustness tests.