This paper provides an econometric examination of technological knowledge spillovers among countries by focusing on the issue of error cross‐sectional dependence, particularly on the different ways—weak and strong—that this dependence may affect model specification and estimation. A preliminary analysis based on estimation of the exponent of cross‐sectional dependence provides a clear result in favor of strong cross‐sectional dependence. This result has relevant implications in terms of econometric modeling and suggests that a factor structure is preferable to a spatial error model. The common correlated effects approach is then used because it remains valid in a variety of situations that are likely to occur, such as the presence of both forms of dependence or the existence of nonstationary factors. According to the estimation results, richer countries benefit more from domestic R&D and geographic spillovers than poorer countries, while smaller countries benefit more from spillovers originating from trade. The results also suggest that when the problem of (possibly many) correlated unobserved factors is addressed the quantity of education no longer has a significant effect. Finally, a comparison of the results with those obtained from a spatial model provides interesting insights into the bias that may arise when we allow only for weak dependence, despite the presence of strong dependence in the data. Copyright © 2016 John Wiley & Sons, Ltd.