Against the background of renewed interest in vertical support policies targeting specific industries or technologies, we investigate the effects of vertical vs. horizontal policies in a combinatorial model of economic development. In the framework we propose, an economy develops by acquiring new capabilities allowing for the production of an ever greater variety of products with an increasing complexity. Innovation policy can aim to expand the number of capabilities (vertical policy) or the ability to combine capabilities (horizontal policy). The model shows that for low-income countries, the two policies are complementary. For high-income countries that are specialised in the most complex products, focusing on horizontal policy only yields the highest returns. We reflect on the model results in the light of the contemporary debate on vertical policy.