Limited access of entrepreneurs to credit constrains the creation and growth of private firms. In Africa, access to credit is particularly limited for small and medium enterprises (SMEs) due to unclear property rights and the lack of assets that can be used as collateral. This paper presents a model where firm creation and growth hinge on matching potential entrepreneurs with productive technologies, while firm growth depends on acquired capital. The shortage of collateral creates a binding credit constraint on borrowing by SMEs and hence private sector growth and employment, even though the banking sectors have ample liquidity, as is the case in many African countries. The model is tested using a sample of 20 African countries over the period 2005-09. The empirical results suggest that policies aimed at easing the binding credit constraints (e.g., the depth of credit information and the strength of legal rights pertaining to collateral and bankruptcy) would stimulate productive entrepreneurship and private sector employment in Africa.