We study a model of lumpy investment wherein establishments face persistent shocks to common and plant‐specific productivity, and nonconvex adjustment costs lead them to pursue generalized (, ) investment rules. We allow persistent heterogeneity in both capital and total factor productivity alongside low‐level investments exempt from adjustment costs to develop the first model consistent with the cross‐sectional distribution of establishment investment rates. Examining the implications of lumpy investment for aggregate dynamics in this setting, we find that they remain substantial when factor supply considerations are ignored, but are quantitatively irrelevant in general equilibrium.